Ranks of elliptic curves in families of quadratic twists.
Rubin, Karl, Silverberg, Alice (2000)
Experimental Mathematics
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Displaying similar documents to “Quadratic twists of elliptic curves with small Selmer rank”
Ranks of elliptic curves in families of quadratic twists.
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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...
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