Construction of high-rank elliptic curves with a nontrivial torsion point

Nagao, Koh-ichi

doi:10.1090/S0025-5718-97-00779-5

Construction of high-rank elliptic curves with a nontrivial torsion point
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Math. Comp. 66 (1997), 411-415 Request permission

Abstract:

We construct a family of infinitely many elliptic curves over $\mathbb {Q}$ with a nontrivial rational 2-torsion point and with rank $\ge$ 6, which is parametrized by the rational points of an elliptic curve of rank $\ge$ 1.

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