Abstract
In this paper, we prove a certain maximality property of the Shimura subgroup amongst the multiplicative-type subgroups of , and apply this to verify conjectures of Stevens on the existence of certain canonical parametrizations of rational elliptic curves by modular curves. We are also able to verify some of Stevens’s conjectures on the characterization of the elliptic curve in an isogeny class with minimal Faltings–Parshin height.AMS 2000 Mathematics subject classification: Primary 11G05; 11G18
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