On the degree of modular parametrizations over function fields

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Abstract

Let E be an elliptic curve over Fq(T) with conductor N · ∞. Let p: X0(N) → E be the modular parametrization by the Drinfeld modular curve of level N. Assuming that E is a strong Weil curve we prove upper and lower bounds on deg p. These bounds are the analogs of well-known (partially conjectural) bounds in the case of rational numbers.

Original languageEnglish (US)
Pages (from-to)317-349
Number of pages33
JournalJournal of Number Theory
Volume97
Issue number2
DOIs
StatePublished - Dec 1 2002

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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