On the degree of modular parametrizations over function fields

Mihran Papikian

doi:10.1016/S0022-314X(02)00016-1

On the degree of modular parametrizations over function fields

Mihran Papikian

Mathematics

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

5 Scopus citations

Abstract

Let E be an elliptic curve over F_q(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 language	English (US)
Pages (from-to)	317-349
Number of pages	33
Journal	Journal of Number Theory
Volume	97
Issue number	2
DOIs	https://doi.org/10.1016/S0022-314X(02)00016-1
State	Published - Dec 1 2002

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/S0022-314X(02)00016-1

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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.",

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AB - 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.

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On the degree of modular parametrizations over function fields

Abstract

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