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arXiv · 1906.10580

Integrality properties in the Moduli Space of Elliptic Curves: CM Case

Stefan Schmid
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Abstract

A result of Habegger shows that there are only finitely many singular moduli such that $j$ or $j-\alpha$ is an algebraic unit. The result uses Duke's Equidistribution Theorem and is thus not effective. For a fixed $j$-invariant $\alpha \in \bar{\mathbb{Q}}$ of an elliptic curve without complex multiplication, we prove that there are only finitely many singular moduli $j$ such that $j-\alpha$ is an algebraic unit. The difference to the work of Habegger is that we give explicit bounds.

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Stefan Schmid. 2019-06-25. Integrality properties in the Moduli Space of Elliptic Curves: CM Case. https://arxiv.org/abs/1906.10580

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