Strong Weil curves over Fq(T) with small conductor

JOURNAL OF NUMBER THEORY

卷:131

Article

Schweizer, Andreas

关键词: Elliptic curve;    Drinfeld modular curve;    Strong Weil uniformization;    Frobenius isogeny;    Bruhat-Tits tree;    Rational elliptic surface;   

DOI  :  10.1016/j.jnt.2010.08.007

来源: Elsevier

【 摘 要 】

We continue work of Gekeler and others on elliptic curves over F-q(T) with conductor infinity. n where n is an element of F-q [T] has degree 3. Because of the Frobenius isogeny there are infinitely many curves in each isogeny class, and we discuss in particular which of these curves is the strong Weil curve with respect to the uniformization by the Drinfeld modular curve X-0(n). As a corollary we obtain that the strong Weil curve E/F-q(T) always gives a rational elliptic surface over (F-q) over bar. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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