Mordell-Weil Groups of Elliptic Curves Over Cyclotomic Fields

1982 ◽  
pp. 237-254 ◽  
Author(s):  
Karl Rubin ◽  
Andrew Wiles
Keyword(s):  
Elliptic Curves ◽  
Cyclotomic Fields

scholarly journals On the units generated by Weierstrass forms

2014 ◽  
Vol 17 (A) ◽  
pp. 303-313
Author(s):  
Ömer Küçüksakallı
Keyword(s):  
Elliptic Curves ◽  
Finite Fields ◽  
Class Numbers ◽  
Cyclotomic Fields ◽  
Curves Over Finite Fields ◽  
Elliptic Units ◽  
Fast Arithmetic

AbstractThere is an algorithm of Schoof for finding divisors of class numbers of real cyclotomic fields of prime conductor. In this paper we introduce an improvement of the elliptic analogue of this algorithm by using a subgroup of elliptic units given by Weierstrass forms. These elliptic units which can be expressed in terms of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x$-coordinates of points on elliptic curves enable us to use the fast arithmetic of elliptic curves over finite fields.

Elliptic Curves

1997 ◽  
Author(s):  
Henry McKean ◽  
Victor Moll
Keyword(s):  
Elliptic Curves

The Joint Universality for L-Functions of Elliptic Curves

2004 ◽  
Vol 9 (4) ◽  
pp. 331-348
Author(s):  
V. Garbaliauskienė
Keyword(s):  
Elliptic Curves ◽  
Rational Numbers ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

A joint universality theorem in the Voronin sense for L-functions of elliptic curves over the field of rational numbers is proved.

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