Tenth Algorithmic Number Theory Symposium ANTSX

Explicit 5descent on elliptic curves
Tom Fisher
Abstract: We compute equations for genus one curves representing nontrivial elements of order 5 in the TateShafarevich 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 5isogeny.
Files available: paper (PDF), Magma code
© 201112 Kiran S. Kedlaya (with thanks to Pierrick Gaudry and Emmanuel ThomÃ©)
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