Rank bias for elliptic curves mod $p$

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.

15 pages, 11 figures

References in corpus (3)

• An on-average Maeda-type conjecture in the level aspect
• Lower-Order Biases Second Moments of Dirichlet Coefficients in Families of $L$-Functions
• Zeroes of quaternionic modular forms and central $L$-values