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Tenth Algorithmic Number Theory Symposium ANTS-X
University of California, San Diego
July 9 – 13, 2012

Tenth Algorithmic Number Theory Symposium (ANTS-X)
July 9 – 13, 2012

Explicit 5-descent on elliptic curves

Tom Fisher

Abstract: We compute equations for genus one curves representing non-trivial elements of order 5 in the Tate-Shafarevich group of an elliptic curve. We explain how to write the equations in terms of Pfaffians and give examples for elliptic curves over the rationals both with and without a rational 5-isogeny.

Files available: paper (PDF), Magma code

© 2011-12 Kiran S. Kedlaya (with thanks to Pierrick Gaudry and Emmanuel Thomé)
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