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