3-torsion and conductor of genus 2 curves
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Abstract:
We give an algorithm to compute the conductor for curves of genus 2. It is based on the analysis of 3-torsion of the Jacobian for genus 2 curves over 2-adic fields.References
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Additional Information
- Tim Dokchitser
- Affiliation: Department of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
- MR Author ID: 733080
- Email: tim.dokchitser@bristol.ac.uk
- Christopher Doris
- Affiliation: Department of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
- Email: christopher.doris@bristol.ac.uk
- Received by editor(s): July 6, 2017
- Received by editor(s) in revised form: February 14, 2018, and April 25, 2018
- Published electronically: November 14, 2018
- Additional Notes:
This research was partially supported by an EPSRC
grant EP/M016838/1 “Arithmetic of hyperelliptic curves” and by GCHQ
- © Copyright 2018 American Mathematical Society
- Journal: Math. Comp. 88 (2019), 1913-1927
- MSC (2010): Primary 11G20; Secondary 14D10, 11F80, 11G30
- DOI: https://doi.org/10.1090/mcom/3387
- MathSciNet review: 3925491