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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On a class of elliptic curves with rank at most two
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by H. E. Rose PDF
Math. Comp. 64 (1995), 1251-1265 Request permission


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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1251-1265
  • MSC: Primary 11G40; Secondary 11G05, 11Y50
  • DOI:
  • MathSciNet review: 1297476