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On the probability of having rational \(\ell\)-isogenies

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Abstract.

We calculate the chance that an elliptic curve over a finite field has a specified number of \(\ell\)-isogenies which emanate from it. We give a partial answer for abelian varieties of arbitrary dimension.

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Authors and Affiliations

  1. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA

    Jeffrey D. Achter

  2. Dpto. Matemáticas, Plaza de la Merced 1, 37008, Salamanca, España

    Daniel Sadornil

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  1. Jeffrey D. Achter
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  2. Daniel Sadornil
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Correspondence to Jeffrey D. Achter.

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Received: 20 September 2007

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Achter, J.D., Sadornil, D. On the probability of having rational \(\ell\)-isogenies. Arch. Math. 90, 511–519 (2008). https://doi.org/10.1007/s00013-008-2598-8

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  • DOI: https://doi.org/10.1007/s00013-008-2598-8

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