Sage Days 18 Coding Sprint Projects
- Compute regulators of elliptic curves over function fields
- Is there an algorithm to enumerate all elliptic curves over a function field of a given conductor?
Implement Tate's algorithm for elliptic curves over the function field \mathbf{F}_p(t).
Implement computation of the 3-Selmer rank of an elliptic curve over \mathbf{Q}.
Compute statistics about distribution of Heegner divisors and Kolyvagin divisors modulo primes p.
- Create a table of images of Galois representations, for elliptic curves and/or Jacobians, in some range.
- Fully implement and optimize variant of Watkins's algorithm for fast computation of Heegner points.
- 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.
- Verify Kolyvagin's conjecture for a specific rank 3 curve.
- Implement an algorithm in Sage to compute Stark-Heegner points.
Compute the higher Heegner point y_5 on the curve 389a provably correctly.
Compute special values of the Gross-Zagier L-function L(f,\chi,s).
- Implement something toward the Pollack et al. overconvergent modular symbols algorithm.
- Compute a Heegner point on the Jacobian of a genus 2 curve