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juin 10, 2004
Elliptic curves with complex multiplication
Here is the text of an announcement for an efficient p-adic algorithm to compute elliptic curves with a given number of points. This is a joined work with Reynald Lercier.
Summary : the heart of the computation is the calculation of the Hilbert class polynomial for a discriminant D. Whereas most the methods compute this polynomial by complex approximation of his roots, we compute p-adic approximations by a way of supersingular reductions. We implemented it for discriminants D of increasing size which are known to be "hard" cases.
More details can be found here in the related archive of the Number Theory Mailing List.
Publié par Emmanuel Riboulet-Deyris à juin 10, 2004 12:31 PM
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