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