Mathematical Research Letters

Volume 13 (2006)

Number 2

On the torsion of optimal elliptic curves over function fields

Pages: 321 – 331

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n2.a12

Author

Mihran Papikian (Stanford University)

Abstract

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 $\deg(\fp)$.

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