Elliptic curves over finite fields. II
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- by I. Borosh, C. J. Moreno and H. Porta PDF
- Math. Comp. 29 (1975), 951-964 Request permission
Abstract:
The class groups of certain elliptic function fields without complex multiplications are computed. Questions about the structure of these groups and the arithmetical nature of their orders are considered.References
- B. J. Birch, Elliptic curves and modular functions, Symposia Mathematica, Vol. IV (INDAM, Rome, 1968/69) Academic Press, London, 1970, pp. 27–32. MR 0269654
- I. Borosh, C. Moreno, and H. Porta, Elliptic curves over finite fields. I, Proceedings of the 1972 Number Theory Conference (Univ. Colorado, Boulder, Colo.), Univ. Colorado, Boulder, Colo., 1972, pp. 147–155. MR 0404263 I. BOROSH, C. MORENO & H. PORTA, "Elliptic curves over finite fields. III." (In preparation.)
- Irving Gerst and John Brillhart, On the prime divisors of polynomials, Amer. Math. Monthly 78 (1971), 250–266. MR 279071, DOI 10.2307/2317521
- J. W. S. Cassels, Diophantine equations with special reference to elliptic curves, J. London Math. Soc. 41 (1966), 193–291. MR 199150, DOI 10.1112/jlms/s1-41.1.193
- J. W. S. Cassels and A. Fröhlich (eds.), Algebraic number theory, Academic Press, London; Thompson Book Co., Inc., Washington, D.C., 1967. MR 0215665
- Koji Doi and Hidehisa Naganuma, On the algebraic curves uniformized by arithmetical automorphic functions, Ann. of Math. (2) 86 (1967), 449–460. MR 219537, DOI 10.2307/1970610
- Barry Mazur, Rational points of abelian varieties with values in towers of number fields, Invent. Math. 18 (1972), 183–266. MR 444670, DOI 10.1007/BF01389815
- A. P. Ogg, Rational points on certain elliptic modular curves, Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 221–231. MR 0337974
- Jean-Pierre Serre, Propriétés galoisiennes des points d’ordre fini des courbes elliptiques, Invent. Math. 15 (1972), no. 4, 259–331 (French). MR 387283, DOI 10.1007/BF01405086
- Goro Shimura, A reciprocity law in non-solvable extensions, J. Reine Angew. Math. 221 (1966), 209–220. MR 188198, DOI 10.1515/crll.1966.221.209
- Jacques Vélu, Courbes elliptiques sur $\textbf {Q}$ ayant bonne réduction en dehors de $\{11\}$, C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A73–A75 (French). MR 316457
- B. F. Wyman, What is a reciprocity law?, Amer. Math. Monthly 79 (1972), 571–586; correction, ibid. 80 (1973), 281. MR 308084, DOI 10.2307/2317083
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 951-964
- MSC: Primary 14G15; Secondary 14K15
- DOI: https://doi.org/10.1090/S0025-5718-1975-0404264-3
- MathSciNet review: 0404264