Rational torsion points on elliptic curves over number fields
Bas Edixhoven (1993-1994)
Séminaire Bourbaki
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Rational torsion points on elliptic curves over number fields
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As a subproduct of the Schoof-Elkies-Atkin algorithm to count points on elliptic curves defined over finite fields of characteristic , there exists an algorithm that computes, for an Elkies prime, -torsion points in an extension of degree at cost bit operations in the favorable case where . We combine in this work a fast algorithm for computing isogenies due to Bostan, Morain, Salvy and Schost with the -adic approach followed by Joux and Lercier to get an algorithm...