Richard Griffon

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20162025

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math.NT2019

Elliptic curves with large Tate-Shafarevich groups over $F_{q} (t)$

Richard Griffon, Guus de Wit

Let $F_{q}$ be a finite field of odd characteristic $p$ . We exhibit elliptic curves over the rational function field $K = F_{q} (t)$ whose Tate-Shafarevich groups are…

math.NT2019

On the arithmetic of a family of twisted constant elliptic curves

Richard Griffon, Douglas Ulmer

Let $F_{r}$ be a finite field of characteristic $p > 3$ . For any power $q$ of $p$ , consider the elliptic curve $E = E_{q, r}$ defined by $y^{2} = x^{3} + t^{q} - t$ over $K=\mathbb{F}_r(t…

Elliptic curves with large Tate-Shafarevich groups over Fq​(t)

On the arithmetic of a family of twisted constant elliptic curves

Elliptic curves with large Tate-Shafarevich groups over $F_{q} (t)$