On quadratic families of CM elliptic curves

Munshi, Ritabrata (2011) On quadratic families of CM elliptic curves Transactions of the American Mathematical Society, 363 . p. 4337. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/2011-363-08/S0002...

Related URL: http://dx.doi.org/10.1090/S0002-9947-2011-05433-4


Given a CM elliptic curve with Weierstrass equation y2 = f(x), and a positive definite binary quadratic form Q(u,v), we show that there are infinitely many reduced integer pairs (u,v) such that the twisted elliptic curve Q(u,v)y2 = f(x) has analytic rank (and consequently Mordell-Weil rank) one. In fact it follows that the number of such pairs with |u|, |v| ≤ X is at least X2-ε for any ε > 0.

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Deposited On:31 Jan 2018 09:08
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