On a class of elliptic curves with rank at most two

Author:
H. E. Rose

Journal:
Math. Comp. **64** (1995), 1251-1265, S27

MSC:
Primary 11G40; Secondary 11G05, 11Y50

DOI:
https://doi.org/10.1090/S0025-5718-1995-1297476-3

MathSciNet review:
1297476

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note we consider the elliptic curves defined over for primes *p* satisfying , and review some of their properties. We then compute and list (in the supplement) their ranks, and give, when the rank is positive, the generators of the group of rational points and Mordell-Weil lattice invariant for all primes of the form .

**[1]**A. Bremner and J. W. S. Cassels,*On the equation*, Math. Comp.**42**(1984), 257-264. MR**726003 (85f:11017)****[2]**A. Bremner,*On the equation*, Number Theory and Applications (R. A. Mollin, ed.), Kluwer, Dordrecht, 1989, pp. 3-23.**[3]**J. Buhler, B. Gross, and D. Zagier,*On the conjecture of Birch and Swinnerton-Dyer for a curve of rank*3, Math. Comp.**44**(1985), 473-481. MR**777279 (86g:11037)****[4]**H. Cohen,*A course in computational algebraic number theory*, Springer, Berlin, 1993. MR**1228206 (94i:11105)****[5]**L. J. Mordell,*The diophantine equation*, Quart. J. Math. (2)**18**(1967), 1-6. MR**0210659 (35:1545)****[6]**H. E. Rose,*On a class of elliptic curves with rank at most two*, University of Bristol preprint, 1992. MR**1297476 (95j:11059)****[7]**K. Rubin,*The one-variable main conjecture for elliptic curves with complex multiplication, L*-functions and Arithmetic (J. Coates and M. J. Taylor, eds.), Cambridge Univ. Press, Cambridge, 1991. MR**1110401 (92j:11055)****[8]**J. H. Silverman,*The arithmetic of elliptic curves*, Springer, New York, 1986. MR**817210 (87g:11070)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1995-1297476-3

Keywords:
Elliptic curve,
rank

Article copyright:
© Copyright 1995
American Mathematical Society