On a class of elliptic curves with rank at most two
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- by H. E. Rose PDF
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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 ${m^2} + 64{n^2}$.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Math. Comp. 64 (1995), 1251-1265
- MSC: Primary 11G40; Secondary 11G05, 11Y50
- DOI: https://doi.org/10.1090/S0025-5718-1995-1297476-3
- MathSciNet review: 1297476