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| * Compute regulators of elliptic curves over function fields | <<TableOfContents>> |
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| * Is there an algorithm to enumerate all elliptic curves over a function field of a given conductor? | == Compute regulators of elliptic curves over function fields == |
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| * Implement Tate's algorithm for elliptic curves over the function field $\mathbf{F}_p(t)$. | People: ''Sal Baig'' |
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| * Implement computation of the 3-Selmer rank of an elliptic curve over $\mathbf{Q}$. | == Is there an algorithm to enumerate all elliptic curves over a function field of a given conductor? == |
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| * Compute statistics about distribution of Heegner divisors and Kolyvagin divisors modulo primes $p$. | People: ''Sal Baig'', William Stein |
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| * 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. | == Implement Tate's algorithm for elliptic curves over the function field F_p(t) == |
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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. | People: ''Sal Baig'', David Roe (?) |
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| * 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 computation of the 3-Selmer rank of an elliptic curve over QQ == |
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| * Compute the higher Heegner point $y_5$ on the curve 389a '''provably correctly'''. | People: ''Robert Miller'', William Stein |
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| * 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. | == Compute statistics about distribution of Heegner divisors and Kolyvagin divisors modulo primes p == |
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| * Compute a Heegner point on the Jacobian of a genus 2 curve | 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: ? |
Sage Days 18 Coding Sprint Projects
Contents
-
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
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: ?