scholarly journals Elliptic curves over real quadratic fields with everywhere good reduction and a non-trivial 3-division point

2013 ◽  
Vol 133 (9) ◽  
pp. 2901-2913 ◽  
Author(s):  
Yu Zhao
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields ◽  
Good Reduction ◽  
Real Quadratic Fields ◽  
Division Point ◽  
Real Quadratic

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.

scholarly journals AN ANALOGUE OF CIRCULAR UNITS FOR PRODUCTS OF ELLIPTIC CURVES

2004 ◽  
Vol 47 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Srinath Baba ◽  
Ramesh Sreekantan
Keyword(s):  
Elliptic Curves ◽  
Class Number ◽  
Quadratic Fields ◽  
Motivic Cohomology ◽  
Real Quadratic Fields ◽  
Quadratic Twists ◽  
Class Number Formula ◽  
Number Formula ◽  
Circular Units ◽  
Real Quadratic

AbstractWe construct certain elements in the motivic cohomology group $H^3_{\mathcal{M}}(E\times E',\mathbb{Q}(2))$, where $E$ and $E'$ are elliptic curves over $\mathbb{Q}$. When $E$ is not isogenous to $E'$ these elements are analogous to circular units in real quadratic fields, as they come from modular parametrizations of the elliptic curves. We then find an analogue of the class-number formula for real quadratic fields, which specializes to the usual quadratic class-number formula when $E$ and $E'$ are quadratic twists.AMS 2000 Mathematics subject classification: Primary 11F67; 14G35. Secondary 11F11; 11E45; 14G10

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