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<https://discovery.ucl.ac.uk/id/eprint/10038649> <http://purl.org/dc/terms/title> "Ranks of quadratic twists of elliptic curves"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10038649> <http://purl.org/ontology/bibo/abstract> "We report on a large-scale project to investigate the ranks of elliptic curves in\r\na quadratic twist family, focussing on the congruent number curve. Our methods to exclude\r\ncandidate curves include 2-Selmer, 4-Selmer, and 8-Selmer tests, the use of the Guinand-Weil\r\nexplicit formula, and even 3-descent in a couple of cases. We find that rank 6 quadratic twists\r\nare reasonably common (though still quite difficult to find), while rank 7 twists seem much\r\nmore rare. We also describe our inability to find a rank 8 twist, and discuss how our results here\r\ncompare to some predictions of rank growth vis-à-vis conductor. Finally we explicate a heuristic\r\nof Granville, which when interpreted judiciously could predict that 7 is indeed the maximal rank\r\nin this quadratic twist family."^^<http://www.w3.org/2001/XMLSchema#string> .
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