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arXiv · 2103.02115

Rank bias for elliptic curves mod $p$

Kimball Martin·Thomas Pharis
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Abstract

We conjecture that, for a fixed prime $p$, rational elliptic curves with higher rank tend to have more points mod $p$. We show that there is an analogous bias for modular forms with respect to root numbers, and conjecture that the order of the rank bias for elliptic curves is greater than that of the root number bias for modular forms.

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Kimball Martin, Thomas Pharis. 2021-03-03. Rank bias for elliptic curves mod $p$. https://doi.org/10.2140/involve.2022.15.709

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