92 citations · 1.1k across the 51 of their papers we have counts for
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On the Distribution of Atkin and Elkies Primes
Igor E. Shparlinski, Andrew V. Sutherland
Given an elliptic curve E over a finite field F_q of q elements, we say that an odd prime ell not dividing q is an Elkies prime for E if t_E^2 - 4q is a square modulo ell, where t_…
Sato-Tate distributions and Galois endomorphism modules in genus 2
Francesc Fité, Kiran S. Kedlaya, Victor Rotger +1
For an abelian surface A over a number field k, we study the limiting distribution of the normalized Euler factors of the L-function of A. This distribution is expected to correspo…
Identifying supersingular elliptic curves
Andrew V. Sutherland
Given an elliptic curve E over a field of positive characteristic p, we consider how to efficiently determine whether E is ordinary or supersingular. We analyze the complexity of s…
A low-memory algorithm for finding short product representations in finite groups
Gaetan Bisson, Andrew V. Sutherland
We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-rho approach. Given an element z and a sequence…
The probability that the number of points on the Jacobian of a genus 2 curve is prime
Wouter Castryck, Amanda Folsom, Hendrik Hubrechts +1
In 2000, Galbraith and McKee heuristically derived a formula that estimates the probability that a randomly chosen elliptic curve over a fixed finite prime field has a prime number…