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arXiv · 1612.06318

The truth about torsion in the CM case, II

Pete L. Clark·Paul Pollack
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Abstract

Let $T_{{\rm CM}}(d)$ be the largest size of the torsion subgroup of an elliptic curve with complex multiplication (CM) defined over a degree $d$ number field. Work of Breuer and Clark--Pollack showed $\limsup_{d \to \infty} \frac{T_{{\rm CM}}(d)}{d \log \log d} \in (0,\infty)$. Here we show that the above limit supremum is precisely $\frac{e^{\gamma} \pi}{\sqrt{3}}$. We also study -- in part, out of necessity -- the upper order of the size of the torsion subgroup of various restricted classes of CM elliptic curves over number fields.

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Pete L. Clark, Paul Pollack. 2016-12-19. The truth about torsion in the CM case, II. https://arxiv.org/abs/1612.06318

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