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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 $\mathbf{F}_p(t)$. == |
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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 $\mathbf{Q}$. == |
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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
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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 $\mathbf{F}_p(t)$.
- 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
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: ?