On the torsion of optimal elliptic curves over function fields

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Abstract

For an optimal elliptic curve E over double-struck F signq(t) of conductor p·∞ where p 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 ≅ ℤ/nℤ for some n, 1 ≤ n ≤ 3, and that n divides (q - 1) and deg(p).

Original languageEnglish (US)
Pages (from-to)321-331
Number of pages11
JournalMathematical Research Letters
Volume13
Issue number2-3
DOIs
Publication statusPublished - Jan 1 2006

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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