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Examples of torsion points on genus two curves


Authors: John Boxall and David Grant
Journal: Trans. Amer. Math. Soc. 352 (2000), 4533-4555
MSC (2000): Primary 11G30, 14H25
DOI: https://doi.org/10.1090/S0002-9947-00-02368-0
Published electronically: June 8, 2000
MathSciNet review: 1621721
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Abstract | References | Similar Articles | Additional Information

Abstract: We describe a method that sometimes determines all the torsion points lying on a curve of genus two defined over a number field and embedded in its Jacobian using a Weierstrass point as base point. We then apply this to the examples $y^{2}=x^{5}+x$, $y^{2}=x^{5}+5\,x^{3}+x$, and $y^{2}-y=x^{5}$.


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Additional Information

John Boxall
Affiliation: CNRS, UPRESA 6081, Département de Mathématiques et de Mécanique, Université de Caen, Boulevard maréchal Juin, B.P. 5186, 14032 Caen cedex, France
Email: boxall@math.unicaen.fr

David Grant
Affiliation: Department of Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309-0395
Email: grant@boulder.colorado.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02368-0
Keywords: Curves of genus two, elliptic curves, torsion, Galois representations
Received by editor(s): October 6, 1997
Received by editor(s) in revised form: April 18, 1998
Published electronically: June 8, 2000
Additional Notes: The first author was enjoying the hospitality of the University of Colorado at Boulder while the paper was completed. The second author was supported by NSF DMS–930322 and was enjoying the hospitality of the University of Caen while conducting part of this research
Article copyright: © Copyright 2000 American Mathematical Society

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