Elliptic curves with common torsion x-coordinates and hyperelliptic torsion packets

Title data

Fu, Hang ; Stoll, Michael:
Elliptic curves with common torsion x-coordinates and hyperelliptic torsion packets.
In: Proceedings of the American Mathematical Society. Vol. 150 (2022) . - pp. 5137-5149.
ISSN 1088-6826
DOI: https://doi.org/10.1090/proc/16102

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Abstract in another language

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 P1x 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.

Further data

Item Type:	Article in a journal
Refereed:	Yes
Keywords:	Elliptic curves; Torsion points; Hyperelliptic curves; Torsion packets
Subject classification:	Mathematics Subject Classification. 11G05, 11G30, 14H40, 14H45, 14H52
Institutions of the University:	Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - Univ.-Prof. Dr. Michael Stoll
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	22 Dec 2023 10:59
Last Modified:	08 Jan 2024 12:36
URI:	https://eref.uni-bayreuth.de/id/eprint/87798