Nonexistence of elliptic curves having good reduction everywhere over certain quadratic fields

2001 ◽  
Vol 76 (6) ◽  
pp. 436-440 ◽  
Author(s):  
M. Kida
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields ◽  
Good Reduction

Modular symbols for 1(N) and elliptic curves with everywhere good reduction

1992 ◽  
Vol 111 (2) ◽  
pp. 199-218 ◽  
Author(s):  
J. E. Cremona
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields ◽  
Cusp Forms ◽  
Modular Curves ◽  
Good Reduction ◽  
Modular Symbols ◽  
Real Quadratic Fields ◽  
Real Quadratic

AbstractThe modular symbols method developed by the author in 4 for the computation of cusp forms for 0(N) and related elliptic curves is here extended to 1(N). Two applications are given: the verification of a conjecture of Stevens 14 on modular curves parametrized by 1(N); and the study of certain elliptic curves with everywhere good reduction over real quadratic fields of prime discriminant, introduced by Shimura and related to Pinch's thesis 10.

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