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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 F_p(t)

• People: Sal Baig, David Roe (?)

Implement computation of the 3-Selmer rank of an elliptic curve over QQ

• 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

Drew Sutherland remarks:

Hi William,

I would definitely be motivated to work on the table of Galois images project that you suggested in your list. I am currently rerunning my previous computations on the Stein-Watkins database using an improved version of the algorithm (just for the mod ell case at the moment, I still want to tweak the mod ell^k code some more). It would be great to get all this data organized and accessible in a useful form, especially while everything is fresh in my mind.

Drew

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, Avner Ash

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

• People: ?