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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 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 y5 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,χ,s). == Compute the higher Heegner point y5 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,χ,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

  1. Sage Days 18 Coding Sprint Projects
    1. Compute regulators of elliptic curves over function fields
    2. Is there an algorithm to enumerate all elliptic curves over a function field of a given conductor?
    3. Implement Tate's algorithm for elliptic curves over the function field Fp(t).
    4. Implement computation of the 3-Selmer rank of an elliptic curve over Q.
    5. Compute statistics about distribution of Heegner divisors and Kolyvagin divisors modulo primes p.
    6. Create a table of images of Galois representations, for elliptic curves and/or Jacobians, in some range.
    7. Fully implement and optimize variant of Watkins's algorithm for fast computation of Heegner points.
    8. 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.
    9. Verify Kolyvagin's conjecture for a specific rank 3 curve.
    10. Implement an algorithm in Sage to compute Stark-Heegner points.
    11. Compute the higher Heegner point y5 on the curve 389a '''provably correctly'''.
    12. Compute special values of the Gross-Zagier L-function L(f,χ,s).
    13. Implement something toward the Pollack et al. overconvergent modular symbols algorithm.
    14. 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 Fp(t).

Implement computation of the 3-Selmer rank of an elliptic curve over 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 y5 on the curve 389a '''provably correctly'''.

Compute special values of the Gross-Zagier L-function L(f,χ,s).

Implement something toward the Pollack et al. overconvergent modular symbols algorithm.

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

dayscambridge2/sprints (last edited 2009-12-23 06:38:37 by was)