Infinite family of elliptic curves of rank at least 4

Details Infinite family of elliptic curves of rank at least 4 Infinite family of elliptic curves of rank at least 4

2009-09-18

arxiv.org/abs/0909.3424v2

Mathematics

Number Theory

14 pages, 2 figures

Scientific paper

We investigate $\mathbb{Q}$-ranks of the elliptic curve $E_t$:
$y^2+txy=x^3+tx^2-x+1$ where $t$ is a rational parameter. We prove that for
infinitely many values of $t$ the rank of $E_t(\mathbb{Q})$ is at least 4.

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