Tamagawa Numbers of elliptic curves with C-13 torsion over quadratic fields (CROSBI ID 247236)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Najman, Filip
engleski
Tamagawa Numbers of elliptic curves with C-13 torsion over quadratic fields
Let E be an elliptic curve over a number field K, cv the Tamagawa number of E at v, and let cE be the product of all cv. Lorenzini proved that v13(cE) is positive for all elliptic curves over quadratic fields with a point of order 13. Krumm conjectured, based on extensive computation, that the 13- adic valuation of cE is even for all such elliptic curves. In this note we prove this conjecture and furthermore prove that there is a unique such curve satisfying v13(cE) = 2.
elliptic curves ; Tamagawa numbers
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Podaci o izdanju
145 (9)
2017.
3747-3753
objavljeno
0002-9939
1088-6826
10.1090/proc/13553