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Currently displaying 1 – 4 of 4

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On the Diophantine equation $x^{2} + 7 = y^{m}$

Samir Siksek; John E. Cremona — 2003

Acta Arithmetica

On a theorem of Mestre and Schoof

John E. Cremona; Andrew V. Sutherland — 2010

Journal de Théorie des Nombres de Bordeaux

A well known theorem of Mestre and Schoof implies that the order of an elliptic curve $E$ over a prime field $𝔽_{q}$ can be uniquely determined by computing the orders of a few points on $E$ and its quadratic twist, provided that $q > 229$ . We extend this result to all finite fields with $q > 49$ , and all prime fields with $q > 29$ .

Computing periods of cusp forms and modular elliptic curves.

Cremona, John E. — 1997

Experimental Mathematics

Visualizing elements in the Shafarevich-Tate group.

Cremona, John E.; Mazur, Barry — 2000