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- W2054037211 abstract "When an elliptic curve E ′ / Q of square-free conductor N has a rational point of odd prime order l ∤ N , Dummigan (2005) in [Du] explicitly constructed a rational point of order l on the optimal curve E , isogenous over Q to E ′ , under some conditions. In this paper, we show that his construction also works unconditionally. And applying it to Heegner points of elliptic curves, we find a family of elliptic curves E ′ / Q such that a positive proportion of quadratic twists of E ′ has (analytic) rank 1. This family includes the infinite family of elliptic curves of the same property in Byeon, Jeon, and Kim (2009) [B-J-K] ." @default.
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- W2054037211 date "2011-03-01" @default.
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- W2054037211 title "Rational torsion on optimal curves and rank-one quadratic twists" @default.
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- W2054037211 doi "https://doi.org/10.1016/j.jnt.2010.10.005" @default.
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