ON THE NUMBER OF n-ISOGENIES OF ELLIPTIC CURVES OVER NUMBER FIELDS

Abstract

We find the number of elliptic curves with a cyclic isogeny of degree n over various number fields by studying the modular curves X0(n). We show that for n = 14, 15, 20, 21, 49 there exist infinitely many quartic fields K such that #Y0(n)(Q) 6= #Y0(n)(K) < ∞. In the case n = 27 we prove that there are infinitely many sextic fields such that #Y0(n)(Q) 6= #Y0… (More)

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Cite this paper

@inproceedings{Mikic2014ONTN, title={ON THE NUMBER OF n-ISOGENIES OF ELLIPTIC CURVES OVER NUMBER FIELDS}, author={Miljen Mikic and Filip Najman}, year={2014} }