No $17$-torsion on elliptic curves over cubic number fields

Pierre Parent

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$K_{2}$ of elliptic curves with sufficient torsion over $Q$

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On Elkies subgroups of $ℓ$ -torsion points in elliptic curves defined over a finite field

Reynald Lercier, Thomas Sirvent (2008)

Journal de Théorie des Nombres de Bordeaux

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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 $p$ , there exists an algorithm that computes, for $ℓ$ an Elkies prime, $ℓ$ -torsion points in an extension of degree $ℓ - 1$ at cost $\tilde{O} (ℓ max {(ℓ, log q)}^{2})$ bit operations in the favorable case where $ℓ \leq p / 2$ . We combine in this work a fast algorithm for computing isogenies due to Bostan, Morain, Salvy and Schost with the $p$ -adic approach followed by Joux and Lercier to get an algorithm...

Displaying similar documents to “No 17 -torsion on elliptic curves over cubic number fields”

Displaying similar documents to “No $17$ -torsion on elliptic curves over cubic number fields”