The rank 0-or-1 conjecture for prime quadratic twists of an elliptic curve

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Let EdE^d denote the quadratic twist of the elliptic curve EE by dd. Consider quadratic twists with ∣d∣|d| prime. Rank 0-or-1 conjecture. 100%100\% of quadratic twists EdE^d where ∣d∣|d| is a prime have rank 00 or 11. This is assumed as a standard conjecture for estimating the asymptotic behaviour of the relevant counting function; the supplied context does not provide a resolution of the conjecture.

References

Primary source

Matija Kazalicki, “Quadratic twists of genus one curves and Diophantine quintuples”, arXiv:2209.12864 (2022).

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