EUDML

In this note, we give simple examples of sets $𝒮$ of quadratic forms that have minimal $𝒮$ -universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh [KKO05] in the negative.

Ranks of quadratic twists of elliptic curves

Mark Watkins; Stephen Donnelly; Noam D. Elkies; Tom Fisher; Andrew Granville; Nicholas F. Rogers — 2014

Publications mathématiques de Besançon

We report on a large-scale project to investigate the ranks of elliptic curves in a quadratic twist family, focussing on the congruent number curve. Our methods to exclude candidate curves include 2-Selmer, 4-Selmer, and 8-Selmer tests, the use of the Guinand-Weil explicit formula, and even 3-descent in a couple of cases. We find that rank 6 quadratic twists are reasonably common (though still quite difficult to find), while rank 7 twists seem much more rare. We also describe our inability to find...

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New directions in enumerative chess problems.

On finite sequences satisfying linear recursions.

Mordell-Weil lattices in characteristic 2. III: A Mordell-Weil lattice of rank 128.

The Mathieu group $M_{12}$ and its pseudogroup extension $M_{13}$ .

Supersingular primes for elliptic curves over real number fields

The automorphism group of the modular curve $X_{0} (63)$

Minimal $𝒮$ -universality criteria may vary in size

Ranks of quadratic twists of elliptic curves