Generic Curves of Small Genus in IP3 are of Maximal Rank.
E. Ballico, Ph. Ellia (1983)
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E. Ballico, Ph. Ellia (1983)
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Edoardo Ballico, Philippe Ellia (1984/85)
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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...
M.S. Narasimhan, H Lange (1984)
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W. BOOTHBY (1968)
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