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A database of genus-2 curves over the rational numbers

Part of: Curves Arithmetic algebraic geometry Computational aspects in algebraic geometry

Published online by Cambridge University Press:  26 August 2016

Andrew R. Booker ,
Jeroen Sijsling ,
Andrew V. Sutherland ,
John Voight  and
Dan Yasaki
Andrew R. Booker
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom email andrew.booker@bristol.ac.uk
Jeroen Sijsling
Affiliation:
Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, USA email sijsling@gmail.com
Andrew V. Sutherland
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA email drew@math.mit.edu
John Voight
Affiliation:
Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, USA email jvoight@gmail.com
Dan Yasaki
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Greensboro, 317 College Avenue, Greensboro, NC 27412, USA email d_yasaki@uncg.edu

Abstract

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We describe the construction of a database of genus- $2$ curves of small discriminant that includes geometric and arithmetic invariants of each curve, its Jacobian, and the associated $L$ -function. This data has been incorporated into the $L$ -Functions and Modular Forms Database (LMFDB).

MSC classification

Primary: 11G30: Curves of arbitrary genus or genus $ne 1$ over global fields 14H45: Special curves and curves of low genus 14Q05: Curves

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