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https://doi.org/10.3336/gm.50.2.05

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

Miljen Mikić orcid id 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


Puni tekst: engleski pdf 160 Kb

str. 333-348

preuzimanja: 502

citiraj


Sažetak

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)< ∞.

Ključne riječi

Elliptic curves; Mordell-Weil group; isogenies

Hrčak ID:

150133

URI

https://hrcak.srce.hr/150133

Datum izdavanja:

29.12.2015.

Posjeta: 1.011 *