Rational points on X_0^+ (p^r)

Abstract : We show how the recent isogeny bounds due to É. Gaudron and G. Rémond allow to obtain the triviality of X_0^+ (p^r)(Q), for r>1 and p a prime exceeding 2.10^{11}. This includes the case of the curves X_split (p). We then prove, with the help of computer calculations, that the same holds true for p in the range 10 < p < 10^{14}, p\neq 13. The combination of those results completes the qualitative study of such sets of rational points undertook in previous papers, with the exception of p=13.
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Contributor : Pierre Parent <>
Submitted on : Wednesday, January 9, 2013 - 5:24:17 PM
Last modification on : Thursday, January 11, 2018 - 6:21:22 AM

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  • HAL Id : hal-00772014, version 1
  • ARXIV : 1104.4641



Yu. Bilu, Pierre Parent, M. Rebolledo. Rational points on X_0^+ (p^r). To appear in Annales de l'Institut Fourier. 16 pages, no figure. 2011. 〈hal-00772014〉



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