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A database of genus-2 curves over the rational numbers

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

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, BristolBS8 1TW, United Kingdom email [email protected]
Jeroen Sijsling
Affiliation:
Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, USA email [email protected]
Andrew V. Sutherland
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA email [email protected]
John Voight
Affiliation:
Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, USA email [email protected]
Dan Yasaki
Affiliation:
Department of Mathematics and Statistics, University of North Carolina at Greensboro, 317 College Avenue, Greensboro, NC 27412, USA email [email protected]

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
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 19 , Special Issue A: Algorithmic Number Theory Symposium XII , 2016 , pp. 235 - 254
Copyright
© The Author(s) 2016 

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