Sage Days 18 Coding Sprint Projects

Compute regulators of elliptic curves over function fields

• People: Sal Baig

Is there an algorithm to enumerate all elliptic curves over a function field of a given conductor?

• People: Sal Baig, William Stein

Implement Tate's algorithm for elliptic curves over the function field $\mathbf{F}_p(t)$.

• People: Sal Baig, David Roe (?)

Implement computation of the 3-Selmer rank of an elliptic curve over $\mathbf{Q}$.

• People: Robert Miller, William Stein

Compute statistics about distribution of Heegner divisors and Kolyvagin divisors modulo primes $p$.

• People: William Stein, Dimitar Jetchev

Create a table of images of Galois representations, for elliptic curves and/or Jacobians, in some range.

• People: Drew Sutherland, William Stein

Fully implement and optimize variant of Watkins's algorithm for fast computation of Heegner points.

• People: William Stein, Robert Bradshaw

Implement code to compute the asymptotic distribution of Kolyvagin classes (from Jared Weinstein's talk); this should be pretty easy, though generalizing to higher rank may be challenging.

• People: Jared Weinstein

Verify Kolyvagin's conjecture for a specific rank 3 curve.

• People: William Stein

Implement an algorithm in Sage to compute Stark-Heegner points.

• People: Mathew Greenberg

Compute the higher Heegner point $y_5$ on the curve 389a '''provably correctly'''.

• People: Robert Bradshaw, William Stein

Compute special values of the Gross-Zagier $L$-function $L(f,\chi,s)$.

• People: Robert Bradshaw

Implement something toward the Pollack et al. overconvergent modular symbols algorithm.

• People: Robert Pollack

Compute a Heegner point on the Jacobian of a genus 2 curve

• People: ?