Counting elliptic curves with an isogeny of degree three
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- by Maggie Pizzo, Carl Pomerance and John Voight HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 7 (2020), 28-42
Abstract:
We count by height the number of elliptic curves over $\mathbb {Q}$ that possess an isogeny of degree $3$.References
- William Duke, Elliptic curves with no exceptional primes, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 8, 813–818 (English, with English and French summaries). MR 1485897, DOI 10.1016/S0764-4442(97)80118-8
- David Grant, A formula for the number of elliptic curves with exceptional primes, Compositio Math. 122 (2000), no. 2, 151–164. MR 1775416, DOI 10.1023/A:1001874400583
- Robert Harron and Andrew Snowden, Counting elliptic curves with prescribed torsion, J. Reine Angew. Math. 729 (2017), 151–170. MR 3680373, DOI 10.1515/crelle-2014-0107
- Wieb Bosma, John Cannon, and Catherine Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), no. 3-4, 235–265. Computational algebra and number theory (London, 1993). MR 1484478, DOI 10.1006/jsco.1996.0125
- B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 33–186 (1978). With an appendix by Mazur and M. Rapoport. MR 488287, DOI 10.1007/BF02684339
- Francesco Pappalardi, A survey on $k$-freeness, Number theory, Ramanujan Math. Soc. Lect. Notes Ser., vol. 1, Ramanujan Math. Soc., Mysore, 2005, pp. 71–88. MR 2131677
- Joseph H. Silverman, The arithmetic of elliptic curves, 2nd ed., Graduate Texts in Mathematics, vol. 106, Springer, Dordrecht, 2009. MR 2514094, DOI 10.1007/978-0-387-09494-6
- Andrew V. Sutherland and David Zywina, Modular curves of prime-power level with infinitely many rational points, Algebra Number Theory 11 (2017), no. 5, 1199–1229. MR 3671434, DOI 10.2140/ant.2017.11.1199
Additional Information
- Maggie Pizzo
- Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
- Email: magdalene.r.pizzo.19@dartmouth.edu
- Carl Pomerance
- Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
- MR Author ID: 140915
- Email: carl.pomerance@dartmouth.edu
- John Voight
- Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
- MR Author ID: 727424
- ORCID: 0000-0001-7494-8732
- Email: jvoight@gmail.com
- Received by editor(s): July 5, 2019
- Received by editor(s) in revised form: December 13, 2019
- Published electronically: March 4, 2020
- Additional Notes: The first author was supported by the Jack Byrne Scholars program at Dartmouth College.
The third author was supported by a Simons Collaboration grant (550029). - Communicated by: Rachel Pries
- © Copyright 2020 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 7 (2020), 28-42
- MSC (2010): Primary 11G05; Secondary 14H52
- DOI: https://doi.org/10.1090/bproc/45
- MathSciNet review: 4071798