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ON POSITIVE PROPORTION OF RANK-ZERO TWISTS OF ELLIPTIC CURVES OVER
$\mathbb{Q}$
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 98 / Issue 2 / April 2015
- Published online by Cambridge University Press:
- 07 November 2014, pp. 281-288
- Print publication:
- April 2015
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- Article
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Extending the idea of Dabrowski [‘On the proportion of rank 0 twists of elliptic curves’, C. R. Acad. Sci. Paris, Ser. I 346 (2008), 483–486] and using the 2-descent method, we provide three general families of elliptic curves over
$\mathbb{Q}$ such that a positive proportion of prime-twists of such elliptic curves have rank zero simultaneously.
