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MAGMA Computational Algebra System

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Next: L-Series Up: Arithmetic Geometry Previous: Elliptic Curves over Finite


Hyperelliptic Curves


Removals and Changes:

  • HyperellipticCurveFromIgusaClebsch now works over number fields.


New Features:

  • A function TwoCoverDescent performs descent by 2-covers on a hyperelliptic curve over a number field. It returns the ``2-Selmer set'' of the curve. (This is not the same as 2-descent on the Jacobian of the curve.) If the 2-Selmer set is empty, the curve has no rational points. It can be applied to hyperelliptic curves of degree 4, providing a way to do 4-descent on elliptic curves over number fields.


next up previous
Next: L-Series Up: Arithmetic Geometry Previous: Elliptic Curves over Finite

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