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Examples of torsion points on genus two curves

Author(s): John Boxall; David Grant
Journal: Trans. Amer. Math. Soc. 352 (2000), 4533-4555.
MSC (2000): Primary 11G30, 14H25
Posted: June 8, 2000
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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: 10.1090/S0002-9947-00-02368-0
PII: S 0002-9947(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
Posted: 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
Copyright of article: Copyright 2000, American Mathematical Society

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