Elliptic Curves over $$\mathbb{C}$$
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[1] Sarah Meiklejohn,et al. Review of an introduction to mathematical cryptography by Jeffrey Hoffstein, Jill Pipher, and Joseph Silverman Springer-Verlag, 2008 , 2010, SIGA.
[2] Richard Taylor,et al. A family of Calabi-Yau varieties and potential automorphy , 2010 .
[3] J. Tate,et al. DUALITY THEOREMS IN GALOIS COHOMOLOGY OVER NUMBER FIELDS , 2010 .
[4] S-ganze Punkte auf elliptischen Kurven , 2009 .
[5] Michael Harris,et al. Automorphy for some l-adic lifts of automorphic mod l Galois representations , 2008 .
[6] Ramarathnam Venkatesan,et al. Non-degeneracy of Pollard Rho Collisions , 2008, ArXiv.
[7] E. Victor Flynn,et al. Descent via isogeny on elliptic curves with large rational torsion subgroups , 2008, J. Symb. Comput..
[8] Jeong Han Kim,et al. A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm , 2007, ANTS.
[9] Tanja Lange,et al. Faster Addition and Doubling on Elliptic Curves , 2007, ASIACRYPT.
[10] Katherine E. Stange. Elliptic nets and elliptic curves , 2007, 0710.1316.
[11] H. Edwards. A normal form for elliptic curves , 2007 .
[12] Katherine E. Stange. The Tate Pairing Via Elliptic Nets , 2007, Pairing.
[13] Ramarathnam Venkatesan,et al. Spectral Analysis of Pollard Rho Collisions , 2006, ANTS.
[14] David Mandell Freeman,et al. Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10 , 2006, ANTS.
[15] J. Milnor. On Lattès Maps , 2004, math/0402147.
[16] J. Cremona,et al. Height difference bounds for elliptic curves over number fields , 2006 .
[17] Gerald J. Janusz,et al. Algebraic Number Fields , 2005 .
[18] A. Weng,et al. Elliptic Curves Suitable for Pairing Based Cryptography , 2005, Des. Codes Cryptogr..
[19] Tanja Lange,et al. Handbook of Elliptic and Hyperelliptic Curve Cryptography , 2005 .
[20] Andreas Enge,et al. Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields , 2004, Journal of Cryptology.
[21] Ebru Bekyel. The density of elliptic curves having a global minimal Weierstrass equation , 2004 .
[22] D. Boneh,et al. Short Signatures from the Weil Pairing , 2001, Journal of Cryptology.
[23] David A. Cox. The Arithmetic-Geometric Mean of Gauss , 2004 .
[24] Alfred Menezes,et al. Guide to Elliptic Curve Cryptography , 2004, Springer Professional Computing.
[25] Edward F. Schaefer,et al. How to do a p-descent on an elliptic curve , 2003 .
[26] Igor E. Shparlinski,et al. Elliptic divisibility sequences , 2003 .
[27] C. Clemens. A Scrapbook of Complex Curve Theory: Second Edition , 2002 .
[28] Douglas Ulmer. Elliptic curves with large rank over function fields , 2001, math/0109163.
[29] Matthew K. Franklin,et al. Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.
[30] Mihir Bellare,et al. The Oracle Diffie-Hellman Assumptions and an Analysis of DHIES , 2001, CT-RSA.
[31] Edlyn Teske. Square-root algorithms for the discrete logarithm problem (a survey) , 2001 .
[32] Atsuko Miyaji,et al. Characterization of Elliptic Curve Traces under FR-Reduction , 2000, ICISC.
[33] Edward F. Schaefer,et al. Computing the p-Selmer group of an elliptic curve , 2000 .
[34] Antoine Joux. A One Round Protocol for Tripartite Diffie-Hellman , 2000, ANTS.
[35] R. Taylor,et al. On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises , 2001, Journal of the American Mathematical Society.
[36] Nigel P. Smart,et al. The Discrete Logarithm Problem on Elliptic Curves of Trace One , 1999, Journal of Cryptology.
[37] Edlyn Teske,et al. A space efficient algorithm for group structure computation , 1998, Math. Comput..
[38] Edlyn Teske,et al. Speeding Up Pollard's Rho Method for Computing Discrete Logarithms , 1998, ANTS.
[39] On the rank of an elliptic surface , 1998 .
[40] Takakazu Satoh,et al. Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves , 1998 .
[41] R. Balasubramanian,et al. The Improbability That an Elliptic Curve Has Subexponential Discrete Log Problem under the Menezes—Okamoto—Vanstone Algorithm , 1998, Journal of Cryptology.
[42] Igor A. Semaev,et al. Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p , 1998, Math. Comput..
[43] K. Nagao. ℚ(T)-rank of elliptic curves and certain limit coming from the local points , 1997 .
[44] Y. Bugeaud. Bounds for the solutions of superelliptic equations , 1997, Compositio Mathematica.
[45] Victor Shoup,et al. Lower Bounds for Discrete Logarithms and Related Problems , 1997, EUROCRYPT.
[46] S. Fermigier. Une courbe elliptique définie sur ℚ de rang ≥ 22 , 1997 .
[47] N. Elkies. Elliptic and modular curves over finite fields and related computational issues , 1997 .
[48] Alfred Menezes,et al. Handbook of Applied Cryptography , 2018 .
[49] W. Narkiewicz. Global Class-Field Theory , 1996 .
[50] J. Manin,et al. THE HASSE-WITT MATRIX OF AN ALGEBRAIC CURVE , 1996 .
[51] Loïc Merel,et al. Bornes pour la torsion des courbes elliptiques sur les corps de nombres , 1996 .
[52] P. Voutier. An Upper Bound for the Size of Integral Solutions to Ym=ƒ(X) , 1995 .
[53] A. Wiles,et al. Ring-Theoretic Properties of Certain Hecke Algebras , 1995 .
[54] A. Wiles. Modular Elliptic Curves and Fermat′s Last Theorem(抜粋) (フェルマ-予想がついに解けた!?) , 1995 .
[55] J. Silverman,et al. S-INTEGER POINTS ON ELLIPTIC CURVES , 1995 .
[56] S. David. Minorations de formes linéaires de logarithmes elliptiques , 1995 .
[57] Douglas R. Stinson,et al. Cryptography: Theory and Practice , 1995 .
[58] R. Schoof. Journal de Theorie des Nombres de Bordeaux 7 (1995), 219{254 , 2022 .
[59] Nigel P. Smart,et al. S-integral points on elliptic curves , 1994, Mathematical Proceedings of the Cambridge Philosophical Society.
[60] Joe W. Harris,et al. Principles of Algebraic Geometry: Griffiths/Principles , 1994 .
[61] G. Frey,et al. A remark concerning m -divisibility and the discrete logarithm in the divisor class group of curves , 1994 .
[62] Attila Pethő,et al. Computing integral points on elliptic curves , 1994 .
[63] N. Tzanakis,et al. Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms , 1994 .
[64] A. Atkin,et al. ELLIPTIC CURVES AND PRIMALITY PROVING , 1993 .
[65] G. Wüstholz,et al. Isogeny estimates for abelian varieties, and finiteness theorems , 1993 .
[66] S. Kamienny,et al. Torsion points on elliptic curves andq-coefficients of modular forms , 1992 .
[67] J. Cremona. Algorithms for Modular Elliptic Curves , 1992 .
[68] Three constructions of rational points onY2=X3±NX , 1992 .
[69] Joe Harris,et al. Definitions of Dimension and Elementary Examples , 1992 .
[70] Paul Vojta. Siegel's theorem in the compact case , 1991 .
[71] François Morain. Building Elliptic Curves Modulo Large Primes , 1991, EUROCRYPT.
[72] Alfred Menezes,et al. Reducing elliptic curve logarithms to logarithms in a finite field , 1991, STOC '91.
[73] R. Devaney,et al. Iteration of Rational Functions , 1991 .
[74] Kenneth A. Ribet,et al. On modular representations of $$(\bar Q/Q)$$ arising from modular forms , 1990 .
[75] G. Wüstholz,et al. Estimating isogenies on elliptic curves , 1990 .
[76] R. Gross. A note on Roth's Theorem , 1990 .
[77] Joseph H. Silverman,et al. The difference between the Weil height and the canonical height on elliptic curves , 1990 .
[78] H. Carayol. Sur les représentations Galoisiennes modulo $\ell$ attachées aux formes modulaires , 1989 .
[79] G. Wüstholz. Multiplicity estimates on group varieties , 1989 .
[80] D. Masser. Specializations of finitely generated subgroups of abelian varieties , 1989 .
[81] G. Frey. Links between solutions of A−B=C and elliptic curves , 1989 .
[82] Karl Rubin,et al. The “main conjectures” of iwasawa theory for imaginary quadratic fields , 1988 .
[83] Joseph H. Silverman,et al. Wieferich's criterion and the abc-conjecture , 1988 .
[84] Joseph H. Silverman,et al. Computing heights on elliptic curves , 1988 .
[85] Takeshi Saito,et al. Conductor, discriminant, and the Noether formula of arithmetic surfaces , 1988 .
[86] M. Brown,et al. Note On Supersingular Primes of Elliptic Curves Over Q , 1988 .
[87] Joseph H. Silverman,et al. The canonical height and integral points on elliptic curves , 1988 .
[88] Joseph H. Silverman,et al. Arithmetic distance functions and height functions in diophantine geometry , 1987 .
[89] G. Frey. Elliptic curves and solutions of A-B=C , 1987 .
[90] Karl Rubin,et al. Tate-Shafarevich groups andL-functions of elliptic curves with complex multiplication , 1987 .
[91] Noam D. Elkies,et al. The existence of infinitely many supersingular primes for every elliptic curve over ℚ , 1987 .
[92] W. Kohnen,et al. Heegner points and derivatives ofL-series. II , 1987 .
[93] Joseph H. Silverman,et al. A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves. , 1987 .
[94] Jean-Pierre Serre. Sur les représentations modulaires de degré $2$ de $\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})$ , 1987 .
[95] Don Zagier,et al. Large Integral Points on Elliptic Curves , 1987 .
[96] N. Koblitz. Elliptic curve cryptosystems , 1987 .
[97] D. W. Masser,et al. Vanishing sums in function fields , 1986, Mathematical Proceedings of the Cambridge Philosophical Society.
[98] Joe Kilian,et al. Almost all primes can be quickly certified , 1986, STOC '86.
[99] Jan-Hendrik Evertse,et al. Uniform bounds for the number of solutions to Yn = f(X) , 1986, Mathematical Proceedings of the Cambridge Philosophical Society.
[100] Don Zagier,et al. Heegner points and derivatives ofL-series , 1986 .
[101] T. Shioda,et al. An Explicit Algorithm for Computing the Picard Number of Certain Algebraic Surfaces , 1986 .
[102] R. C. Mason. Norm form equations I , 1986 .
[103] R. Pinch. Elliptic curves with good reduction away from 2: II , 1984, Mathematical Proceedings of the Cambridge Philosophical Society.
[104] Gerd Faltings,et al. Finiteness Theorems for Abelian Varieties over Number Fields , 1986 .
[105] Ted Chinburg,et al. An Introduction to Arakelov Intersection Theory , 1986 .
[106] Paul Vojta,et al. A Higher Dimensional Mordell Conjecture , 1986 .
[107] José Felipe Voloch,et al. Diagonal equations over function fields , 1985 .
[108] Victor S. Miller,et al. Use of Elliptic Curves in Cryptography , 1985, CRYPTO.
[109] Joseph H. Silverman,et al. Divisibility of the Specialization Map for Families of Elliptic Curves , 1985 .
[110] Don Zagier,et al. On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank 3 , 1985 .
[111] R. Schoof. Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p , 1985 .
[112] D V Chudnovsky,et al. Padé approximations and diophantine geometry. , 1985, Proceedings of the National Academy of Sciences of the United States of America.
[113] N. Katz,et al. Arithmetic Moduli of Elliptic Curves. (AM-108) , 1985 .
[114] Joseph H. Silverman,et al. Weierstrass equations and the minimal discriminant of an elliptic curve , 1984 .
[115] Jan-Hendrik Evertse,et al. On equations inS-units and the Thue-Mahler equation , 1984 .
[116] D. Rohrlich,et al. OnL-functions of elliptic curves and cyclotomic towers , 1984 .
[117] T. Elgamal. A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.
[118] Adi Shamir,et al. Identity-Based Cryptosystems and Signature Schemes , 1984, CRYPTO.
[119] Gerd Faltings,et al. Calculus on arithmetic surfaces , 1984 .
[120] Joseph H. Silverman. The S -unit equation over function fields , 1984 .
[121] G. Wüstholz,et al. Recent progress in transcendence theory , 1984 .
[122] Andrew Bremner,et al. On the equation , 1984 .
[123] J. W. S. Cassels,et al. On the equation , 1984 .
[124] G. Faltings. Endlichkeitssätze für abelsche Varietäten über Zahlkörpern , 1983 .
[125] David Masser,et al. Fields of large transcendence degree generated by values of elliptic functions , 1983 .
[126] S. Lang. Fundamentals of Diophantine Geometry , 1983 .
[127] J. Silverman. Integer Points on Curves of Genus 1 , 1983 .
[128] P. Erdös,et al. On a problem of Oppenheim concerning “factorisatio numerorum” , 1983 .
[129] R. Greenberg. On the Birch and Swinnerton-Dyer conjecture , 1983 .
[130] R. C. Mason. The hyperelliptic equation over function fields , 1983, Mathematical Proceedings of the Cambridge Philosophical Society.
[131] J. Tate,et al. Variation of the Canonical Height of a Point Depending on a Parameter , 1983 .
[132] Adi Shamir,et al. A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.
[133] S. Lang,et al. Conjectured Diophantine Estimates on Elliptic Curves , 1983 .
[134] Michael Laska. Elliptic curves over number fields with prescribed reduction type , 1983 .
[135] Joseph H. Silverman,et al. Heights and the specialization map for families of abelian varieties. , 1983 .
[136] M. A Kenku. On the number of Q-isomorphism classes of elliptic curves in each Q-isogeny class , 1982 .
[137] L. V. Danilov. Diophantine equation x3−y2=k and Hall's conjecture , 1982 .
[138] Kenneth S. Brown,et al. Cohomology of Groups , 1982 .
[139] Jean-François Mestre. Courbes elliptiques et formules explicites , 1982 .
[140] Michael Laska,et al. An algorithm for finding a minimal Weierstrass equation for an elliptic curve , 1982 .
[141] Jean-Pierre Serre,et al. Quelques applications du théorème de densité de Chebotarev , 1981 .
[142] Karl Rubin,et al. Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer , 1981 .
[143] Joseph H. Silverman,et al. Lower bound for the canonical height on elliptic curves , 1981 .
[144] W. W. Stothers,et al. POLYNOMIAL IDENTITIES AND HAUPTMODULN , 1981 .
[145] Stephen Hoel Schanuel. Heights in number fields , 1979 .
[146] Stephen C. Pohlig,et al. An Improved Algorithm for Computing Logarithms over GF(p) and Its Cryptographic Significance , 2022, IEEE Trans. Inf. Theory.
[147] J. Pollard,et al. Monte Carlo methods for index computation () , 1978 .
[148] B. Mazur,et al. Rational isogenies of prime degree , 1978 .
[149] Nicole Arthaud,et al. On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I , 1978 .
[150] Joe W. Harris,et al. Principles of Algebraic Geometry , 1978 .
[151] Bennett Setzer,et al. Elliptic curves over complex quadratic fields , 1978 .
[152] Armand Brumer,et al. The rank of elliptic curves , 1977 .
[153] Barry Mazur,et al. Modular curves and the eisenstein ideal , 1977 .
[154] Whitfield Diffie,et al. New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.
[155] D. Kubert. Universal Bounds on the Torsion of Elliptic Curves , 1976 .
[156] Horst G. Zimmer,et al. On the difference of the Weil height and the Néron-Tate height , 1976 .
[157] T. Apostol. Introduction to analytic number theory , 1976 .
[158] T. Apostol. Modular Functions and Dirichlet Series in Number Theory , 1976 .
[159] Bennett Setzer. Elliptic Curves of Prime Conductor , 1975 .
[160] Loren D. Olson. Torsion points on elliptic curves with given j-invariant , 1975 .
[161] D. Masser. Elliptic Functions and Transcendence , 1975 .
[162] B. Birch,et al. Modular Functions of One Variable IV , 1975 .
[163] H. Swinnerton-Dyer,et al. Ellitpic curves and modular functions , 1975 .
[164] J. Tate,et al. Algorithm for determining the type of a singular fiber in an elliptic pencil , 1975 .
[165] P. Deligne. La conjecture de Weil. I , 1974 .
[166] J. Tate,et al. The arithmetic of elliptic curves , 1974 .
[167] I. Shafarevich. Basic algebraic geometry , 1974 .
[168] Jean-Pierre Serre. A Course in Arithmetic , 1973 .
[169] H. M. Stark,et al. Effective estimates of solutions of some diophantine equations , 1973 .
[170] Alain Robert. Elliptic Curves: Notes from Postgraduate Lectures Given in Lausanne 1971/72 , 1973 .
[171] Ju. Manin,et al. CYCLOTOMIC FIELDS AND MODULAR CURVES , 1971 .
[172] Jean-Pierre Serre. Propriétés galoisiennes des points d'ordre fini des courbes elliptiques , 1971 .
[173] G. Shimura. V. The Zeta Function of an Abelian Variety with Complex Multiplication , 1971 .
[174] G. Shimura. On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields , 1971, Nagoya Mathematical Journal.
[175] O. Neumann. Elliptische Kurven mit vorgeschriebenem Reduktionsverhalten. II , 1971 .
[176] André Weil,et al. Dirichlet Series and Automorphic Forms , 1971 .
[177] J. Coates,et al. Construction of rational functions on a curve , 1970, Mathematical Proceedings of the Cambridge Philosophical Society.
[178] J. Coates,et al. Integer points on curves of genus 1 , 1970, Mathematical Proceedings of the Cambridge Philosophical Society.
[179] Ju. Manin,et al. THE p-TORSION OF ELLIPTIC CURVES IS UNIFORMLY BOUNDED , 1969 .
[180] L. Mordell,et al. Diophantine equations , 1969 .
[181] A. Ogg,et al. Modular forms and Dirichlet series , 1969 .
[182] Michael Francis Atiyah,et al. Introduction to commutative algebra , 1969 .
[183] Jean-Pierre Serre,et al. Good reduction of abelian varieties , 1968 .
[184] A N Paršin,et al. ALGEBRAIC CURVES OVER FUNCTION FIELDS. I , 1968 .
[185] S. Lichtenbaum,et al. THE PERIOD-INDEX PROBLEM FOR ELLIPTIC CURVES. , 1968 .
[186] B. J. Birch,et al. How the Number of Points of An Elliptic Curve Over a Fixed Prime Field Varies , 1968 .
[187] N. Stephens,et al. The diophantine equation X3 + Y3 = DZ3 and the conjectures of Birch and Swinnerton-Dyer. , 1968 .
[188] André Weil,et al. Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen , 1967 .
[189] L. J. Mordell. THE DIOPHANTINE EQUATION x4+my4 =z2 , 1967 .
[190] A. Ogg,et al. ELLIPTIC CURVES AND WILD RAMIFICATION. , 1967 .
[191] A. Ogg. Abelian curves of small conductor. , 1967 .
[192] W. J. Blundon,et al. Numerical solutions of the Diophantine equation , 1966 .
[193] A. Ogg. Abelian curves of 2-power conductor , 1966, Mathematical Proceedings of the Cambridge Philosophical Society.
[194] J. Tate. Endomorphisms of abelian varieties over finite fields , 1966 .
[195] J. Cassels,et al. Diophantine Equations with Special Reference To Elliptic Curves , 1966 .
[196] A. Neron,et al. Quasi-fonctions et Hauteurs sur les Varietes Abeliennes , 1965 .
[197] J. Cassels,et al. Arithmetic on curves of genus 1. VIII. On conjectures of Birch and Swinnerton-Dyer. , 1965 .
[198] J. Tate,et al. Algebraic cycles and poles of zeta functions , 1965 .
[199] D. Mumford,et al. Geometric Invariant Theory , 2011 .
[200] André Néron,et al. Modèles minimaux des variétés abéliennes sur les corps locaux et globaux , 1964 .
[201] J. Cassels,et al. Arithmetic on Curves of Genus 1 (V). Two Counter-Examples , 1963 .
[202] H. Swinnerton-Dyer,et al. Notes on elliptic curves. II. , 1963 .
[203] J. W. S. Cassels,et al. arithmetic on curves of genus 1 : iii. the tate‐Šafarevič and selmer groups , 1962 .
[204] J. Cassels,et al. Arithmetic on Curves of Genus 1. IV. Proof of the Hauptvermutung. , 1962 .
[205] D. Lewis,et al. On the representation of integers by binary forms , 1961 .
[206] Bernard Dwork,et al. On the Rationality of the Zeta Function of an Algebraic Variety , 1960 .
[207] S. Lang,et al. Principal Homogeneous Spaces Over Abelian Varieties , 1958 .
[208] J Igusa,et al. CLASS NUMBER OF A DEFINITE QUATERNION WITH PRIM DISCRIMINANT. , 1958, Proceedings of the National Academy of Sciences of the United States of America.
[209] Par Goro Shimura. Correspondances modulaires et les fonctions ζ de courbes algebriques , 1958 .
[210] Jean-Pierre Serre. Géométrie algébrique et géométrie analytique , 1956 .
[211] Andre Weil. On Algebraic Groups and Homogeneous Spaces , 1955 .
[212] Ernst S. Selmer,et al. A conjecture concerning rational points on cubic curves , 1954 .
[213] Ernst S. Selmer,et al. The diophantine equationax3+by3+cz3=0. Completion of the tables , 1954 .
[214] M. Eichler,et al. Quaternäre quadratische Formen und die Riemannsche Vermutung fÜr die Kongruenzzetafunktion , 1954 .
[215] Jean-Pierre Serre,et al. Cohomology of group extensions , 1953 .
[216] André Weil,et al. Jacobi sums as “Grössencharaktere” , 1952 .
[217] André Néron,et al. Problèmes arithmétique et géométriques rattachés à la notion de rang d'une courbe algébrique dans un corps , 1952 .
[218] Ernst S. Selmer,et al. The diophantine equationax3+by3+cz3=0. , 1951 .
[219] R. J. Walker. Algebraic curves , 1950 .
[220] A. Weil. Numbers of solutions of equations in finite fields , 1949 .
[221] J. W. S. Cassels,et al. A note on the division values of ℘(u) , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.
[222] Morgan Ward,et al. Memoir on Elliptic Divisibility Sequences , 1948 .
[223] Hans Reichardt,et al. Einige im Kleinen überall lösbare, im Großen unlösbare diophantische Gleichungen. , 1942 .
[224] M. Deuring. Die Typen der Multiplikatorenringe elliptischer Funktionenkörper , 1941 .
[225] E. Wright,et al. An Introduction to the Theory of Numbers , 1939 .
[226] K. Mahler,et al. On the Lattice-Points on Curves of Genus , 1935 .
[227] R. Fueter,et al. Ueber kubische diophantische Gleichungen , 1930 .
[228] K. Zsigmondy,et al. Zur Theorie der Potenzreste , 1892 .
[229] G. L. Dirichlet. Ueber den biquadratischen Character der Zahl "Zwei". , 1860 .