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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Elliptic curves with common torsion $x$-coordinates and hyperelliptic torsion packets
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by Hang Fu and Michael Stoll PDF
Proc. Amer. Math. Soc. 150 (2022), 5137-5149 Request permission


We establish a connection between torsion packets on curves of genus $2$ and pairs of elliptic curves realized as double covers of the projective line $\mathbb {P}^1_x$ that have many common torsion $x$-coordinates. This can be used to show that the set of common torsion $x$-coordinates has size at least $22$ infinitely often and has $34$ elements in some cases. We also explain how we obtained the current record example of a hyperelliptic torsion packet on a genus $2$ curve.
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Additional Information
  • Hang Fu
  • Affiliation: Department of Mathematics, National Taiwan University, Taipei, Taiwan
  • MR Author ID: 1172768
  • ORCID: 0000-0002-1214-4664
  • Email:
  • Michael Stoll
  • Affiliation: Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
  • MR Author ID: 325630
  • ORCID: 0000-0001-5868-2962
  • Email:
  • Received by editor(s): September 2, 2021
  • Received by editor(s) in revised form: February 22, 2022
  • Published electronically: September 9, 2022
  • Communicated by: Amanda Folsom
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 5137-5149
  • MSC (2020): Primary 11G05, 11G30, 14H40, 14H45, 14H52
  • DOI: