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- W2890596163 abstract "Let $mathbb{F}_q$ be a finite field of odd characteristic and $K= mathbb{F}_q(t)$. For any integer $dgeq 2$ coprime to $q$, consider the elliptic curve $E_d$ over $K$ defined by $y^2=x(x^2+t^{2d} x-4t^{2d})$. We show that the rank of the Mordell--Weil group $E_d(K)$ is unbounded as $d$ varies. The curve $E_d$ satisfies the BSD conjecture, so that its rank equals the order of vanishing of its $L$-function at the central point. We provide an explicit expression for the $L$-function of $E_d$, and use it to study this order of vanishing in terms of $d$." @default.
- W2890596163 created "2018-09-27" @default.
- W2890596163 creator A5039125058 @default.
- W2890596163 date "2018-09-20" @default.
- W2890596163 modified "2023-09-27" @default.
- W2890596163 title "A new family of elliptic curves with unbounded rank." @default.
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