Glasnik matematički, Vol. 50 No. 2, 2015.
Original scientific paper
https://doi.org/10.3336/gm.50.2.05
ON THE NUMBER OF N-ISOGENIES OF ELLIPTIC CURVES OVER NUMBER FIELDS
Miljen Mikić
orcid.org/0000-0003-4657-0642
; Kumičićeva 20, 51000 Rijeka, Croatia
Filip Najman
; Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
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)≠ # Y0(n)(K)< ∞ . In the case n=27 we prove that there are infinitely many sextic fields such that # Y0(n)(Q)≠ # Y0(n)(K)< ∞.
Keywords
Elliptic curves; Mordell-Weil group; isogenies
Hrčak ID:
150133
URI
Publication date:
29.12.2015.
Visits: 1.026 *