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Counting elliptic curves over the rationals with a 7-isogeny

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Abstract

We count by height the number of elliptic curves over the rationals, both up to isomorphism over the rationals and over an algebraic closure thereof, that admit a cyclic isogeny of degree 7.

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Acknowledgements

The authors would like to thank Eran Assaf, Jesse Elliott, Mits Kobayashi, David Lowry-Duda, Robert Lemke Oliver, Taylor Petty, Tristan Phillips, Carl Pomerance, and Rakvi for their helpful comments. The authors were supported by a Simons Collaboration Grant (550029, to JV).

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  1. Department of Mathematics, Dartmouth College, Hanover, NH, 03755-3551, USA

    Grant Molnar & John Voight

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  1. Grant Molnar
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  2. John Voight
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Correspondence to Grant Molnar.

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Molnar, G., Voight, J. Counting elliptic curves over the rationals with a 7-isogeny. Res. number theory 9, 75 (2023). https://doi.org/10.1007/s40993-023-00482-6

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