Conjectures on elliptic curves over quadratic fields

1979 ◽  
pp. 108-118 ◽  
Author(s):  
Dorian Goldfeld
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields

scholarly journals Torsion points on elliptic curves over all quadratic fields. II

1986 ◽  
Vol 79 ◽  
pp. 119-122 ◽  
Author(s):  
Sheldon Kamienny
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields ◽  
Torsion Points

scholarly journals p-Torsion points on elliptic curves defined over quadratic fields

1984 ◽  
Vol 96 ◽  
pp. 139-165 ◽  
Author(s):  
Fumiyuki Momose
Keyword(s):  
Elliptic Curves ◽  
Prime Number ◽  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Quadratic Fields ◽  
Finite Degree ◽  
Torsion Points

Let p be a prime number and k an algebraic number field of finite degree d. Manin [14] showed that there exists an integer n = n(k,p) (≧0) which satisfies the condition

scholarly journals The non-existence of elliptic curves with everywhere good reduction over certain quadratic fields

1986 ◽  
Vol 12 (1) ◽  
pp. 45-52 ◽  
Author(s):  
Hidenori ISHII
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields ◽  
Good Reduction

scholarly journals On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields

2016 ◽  
Vol 111 (4) ◽  
pp. 1177-1185 ◽  
Author(s):  
Andrej Dujella ◽  
Mirela Jukić Bokun ◽  
Ivan Soldo
Keyword(s):  
Elliptic Curves ◽  
Torsion Group ◽  
Quadratic Fields ◽  
Diophantine Triples

scholarly journals Some Rank Records for Elliptic Curves with Prescribed Torsion Over Quadratic Fields

2014 ◽  
Vol 22 (1) ◽  
pp. 215-219
Author(s):  
Filip Najman
Keyword(s):  
Elliptic Curves ◽  
Torsion Group ◽  
Quadratic Fields

AbstractIn this paper we construct elliptic curves over quadratic fields with prescribed torsion group and record rank. We do this using theoretical arguments and keeping lengthy computations to a minimum.

On the Weierstrass Class of Semistable Elliptic Curves Over Quadratic Fields

1994 ◽  
Vol 26 (2) ◽  
pp. 137-139
Author(s):  
Salvador Comalada
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields

scholarly journals Elliptic curves over quadratic fields with fixed torsion subgroup and positive rank

2012 ◽  
Vol 47 (2) ◽  
pp. 277-284
Author(s):  
Mirela Jukic Bokun
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields ◽  
Torsion Subgroup ◽  
Positive Rank
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