Parametrizing elliptic curves by modular units
Abstract
It is well-known that every elliptic curve over the rationals admits a parametrization by means of modular functions. In this short note, we show that only finitely many elliptic curves over Q can be parametrized by modular units. This answers a question raised by Zudilin in a recent work on Mahler measures. Further, we give the list of all elliptic curves E of conductor up to 1000 parametrized by modular units supported in the rational torsion subgroup of E. Finally, we raise several open questions.
Domains
Mathematics [math]
Origin : Files produced by the author(s)
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