Mathematical Research Letters
Volume 13 (2006)
On the torsion of optimal elliptic curves over function fields
Pages: 321 – 331
For an optimal elliptic curve $E$ over $\F_q(t)$ of conductor $\fp\cdot\infty$, where $\fp$ is prime, we show that $E(F)_\tor$ is generated by the image of the cuspidal divisor group. We also show that $E(F)_\tor\cong \Z/n\Z$ for some $n$, $1 \leq n\leq 3$, and that $n$ divides $(q-1)$ and $\deg(\fp)$.