scholarly journals On high rank $\pi/3$ and $2\pi/3$-congruent number elliptic curves

2014 ◽  
Vol 44 (6) ◽  
pp. 1867-1880 ◽  
Author(s):  
A.S. Janfada ◽  
S. Salami ◽  
A. Dujella ◽  
J.C. Peral
Keyword(s):  
Elliptic Curves ◽  
High Rank ◽  
Congruent Number

scholarly journals High rank elliptic curves of the form y2= x3+Bx

2000 ◽  
Vol 13 (1) ◽  
Author(s):  
J.C. Peral ◽  
J. Aguirre ◽  
CASTAÑEDA F. Castañeda F.
Keyword(s):  
Elliptic Curves ◽  
High Rank

Congruent Number Elliptic Curves with Rank at Least Three

2010 ◽  
Vol 53 (4) ◽  
pp. 661-666 ◽  
Author(s):  
Jennifer A. Johnstone ◽  
Blair K. Spearman
Keyword(s):  
Elliptic Curves ◽  
Infinite Family ◽  
Congruent Number

AbstractWe give an infinite family of congruent number elliptic curves each with rank at least three.

scholarly journals Elliptic Curves of High Rank with Nontrivial Torsion Group over Q

2001 ◽  
Vol 10 (3) ◽  
pp. 475-480 ◽  
Author(s):  
Leopoldo Kulesz ◽  
Colin Stahlke
Keyword(s):  
Elliptic Curves ◽  
Torsion Group ◽  
High Rank

scholarly journals High rank elliptic curves with torsion group $\mathbb {Z}/(2\mathbb {Z})$

2003 ◽  
Vol 73 (245) ◽  
pp. 323-331 ◽  
Author(s):  
Julián Aguirre ◽  
Fernando Castañeda ◽  
Juan Carlos Peral
Keyword(s):  
Elliptic Curves ◽  
Torsion Group ◽  
High Rank

scholarly journals Ordinary elliptic curves of high rank over with constant j-invariant

2004 ◽  
Vol 114 (4) ◽  
Author(s):  
Irene I. Bouw ◽  
Claus Diem ◽  
Jasper Scholten
Keyword(s):  
Elliptic Curves ◽  
High Rank

scholarly journals Right triangles with algebraic sides and elliptic curves over number fields

2009 ◽  
Vol 59 (3) ◽  
Author(s):  
E. Girondo ◽  
G. González-Diez ◽  
E. González-Jiménez ◽  
R. Steuding ◽  
J. Steuding
Keyword(s):  
Positive Integer ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Infinite Order ◽  
Number Fields ◽  
Explicit Construction ◽  
Congruent Number ◽  
Number Problem ◽  
Weil Group ◽  
Congruent Number Problem

AbstractGiven any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem. The proof allows the explicit construction of these triangles; for this purpose we find for any positive integer n an explicit cubic number field ℚ(λ) (depending on n) and an explicit point P λ of infinite order in the Mordell-Weil group of the elliptic curve Y 2 = X 3 − n 2 X over ℚ(λ).

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