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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 icon 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: 297* citiraj
APA 6th Edition
Mikić, M. i Najman, F. (2015). ON THE NUMBER OF N-ISOGENIES OF ELLIPTIC CURVES OVER NUMBER FIELDS. Glasnik matematički, 50 (2), 333-348. https://doi.org/10.3336/gm.50.2.05
MLA 8th Edition
Mikić, Miljen i Filip Najman. "ON THE NUMBER OF N-ISOGENIES OF ELLIPTIC CURVES OVER NUMBER FIELDS." Glasnik matematički, vol. 50, br. 2, 2015, str. 333-348. https://doi.org/10.3336/gm.50.2.05. Citirano 27.10.2021.
Chicago 17th Edition
Mikić, Miljen i Filip Najman. "ON THE NUMBER OF N-ISOGENIES OF ELLIPTIC CURVES OVER NUMBER FIELDS." Glasnik matematički 50, br. 2 (2015): 333-348. https://doi.org/10.3336/gm.50.2.05
Harvard
Mikić, M., i Najman, F. (2015). 'ON THE NUMBER OF N-ISOGENIES OF ELLIPTIC CURVES OVER NUMBER FIELDS', Glasnik matematički, 50(2), str. 333-348. https://doi.org/10.3336/gm.50.2.05
Vancouver
Mikić M, Najman F. ON THE NUMBER OF N-ISOGENIES OF ELLIPTIC CURVES OVER NUMBER FIELDS. Glasnik matematički [Internet]. 2015 [pristupljeno 27.10.2021.];50(2):333-348. https://doi.org/10.3336/gm.50.2.05
IEEE
M. Mikić i F. Najman, "ON THE NUMBER OF N-ISOGENIES OF ELLIPTIC CURVES OVER NUMBER FIELDS", Glasnik matematički, vol.50, br. 2, str. 333-348, 2015. [Online]. https://doi.org/10.3336/gm.50.2.05

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

Posjeta: 500 *