Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian |
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| Authors: | Edward F. Schaefer Joseph L. Wetherell |
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| Affiliation: | a Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, CA 95053, USA
b Center for Communications Research, 4320 Westerra Court, San Diego, CA 92121, USA |
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| Abstract: | This article describes an algorithm for computing the Selmer group of an isogeny between abelian varieties. This algorithm applies when there is an isogeny from the image abelian variety to the Jacobian of a curve. The use of an auxiliary Jacobian simplifies the determination of locally trivial cohomology classes. An example is presented where the rational solutions to x4+(y2+1)(x+y)=0 are determined. |
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| Keywords: | primary 11G10 secondary 11G30 11G35 14G25 |
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