On the torsion of optimal elliptic curves over function fields

Mihran Papikian

doi:10.4310/MRL.2006.v13.n2.a12

On the torsion of optimal elliptic curves over function fields

Mihran Papikian

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

For an optimal elliptic curve E over double-struck F sign_q(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 language	English (US)
Pages (from-to)	321-331
Number of pages	11
Journal	Mathematical Research Letters
Volume	13
Issue number	2-3
DOIs	https://doi.org/10.4310/MRL.2006.v13.n2.a12
State	Published - 2006

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4310/MRL.2006.v13.n2.a12

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title = "On the torsion of optimal elliptic curves over function fields",

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).",

author = "Mihran Papikian",

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N2 - 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).

AB - 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).

UR - https://www.scopus.com/pages/publications/33746133667

UR - https://www.scopus.com/pages/publications/33746133667#tab=citedBy

U2 - 10.4310/MRL.2006.v13.n2.a12

DO - 10.4310/MRL.2006.v13.n2.a12

M3 - Article

AN - SCOPUS:33746133667

SN - 1073-2780

VL - 13

SP - 321

EP - 331

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 2-3

ER -

On the torsion of optimal elliptic curves over function fields

Abstract

All Science Journal Classification (ASJC) codes

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