Tom Fisher's Home Page

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.

Explicit 5-descent on elliptic curves   (17 pages)          

---

A Magma file giving further details of the example in Section 6 is available here.