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On the number of n-isogenies of elliptic curves over number fields (CROSBI ID 235376)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Mikić, Miljen ; Najman, Filip
On the number of n-isogenies of elliptic curves over number fields // Glasnik matematički, 50 (2015), 2; 333-348. doi: 10.3336/gm.50.2.05
Podaci o odgovornosti
Mikić, Miljen ; Najman, Filip
engleski
On the number of n-isogenies of elliptic curves over number fields
We fi nd the number of elliptic curves with a cyclic isogeny of degree n over various number fields by studying the modular curves X_0(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)< ∞.
Elliptic curves ; Isogenies
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