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Mathematics of Computation

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On a class of elliptic curves with rank at most two

Author: H. E. Rose
Journal: Math. Comp. 64 (1995), 1251-1265
MSC: Primary 11G40; Secondary 11G05, 11Y50
MathSciNet review: 1297476
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Abstract: In this note we consider the elliptic curves ${y^2} = {x^3} + px$ defined over $\mathbb {Q}$ for primes p satisfying $p \equiv 1\; \pmod 8$, 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 $\tau$ for all primes $p < 50000$ of the form ${m^2} + 64{n^2}$.

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Keywords: Elliptic curve, rank
Article copyright: © Copyright 1995 American Mathematical Society