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Mathematics of Computation

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3-torsion and conductor of genus 2 curves


Authors: Tim Dokchitser and Christopher Doris
Journal: Math. Comp. 88 (2019), 1913-1927
MSC (2010): Primary 11G20; Secondary 14D10, 11F80, 11G30
DOI: https://doi.org/10.1090/mcom/3387
Published electronically: November 14, 2018
MathSciNet review: 3925491
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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.


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Additional Information

Tim Dokchitser
Affiliation: Department of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
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

DOI: https://doi.org/10.1090/mcom/3387
Keywords: Conductor, hyperelliptic curves, 3-torsion, local fields
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
Article copyright: © Copyright 2018 American Mathematical Society