11 citations · 32 across the 8 of their papers we have counts for
8 papers · 1 filter
An elliptic curve over Q(u) with torsion Z/4Z and rank 6
Andrej Dujella, Juan Carlos Peral
In this note we present the main details of the construction of an elliptic curve over with torsion and rank 6. Previously only rank 5 exam…
High rank elliptic curves induced by rational Diophantine triples
Andrej Dujella, Juan Carlos Peral
A rational Diophantine triple is a set of three nonzero rational a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares. We say that the elliptic curve y^2 = (ax+1)(bx+1…
Elliptic curves induced by Diophantine triples
Andrej Dujella, Juan Carlos Peral
Given a Diophantine triple , the elliptic curve over Q(t) induced by this triple, i.e. , can have as torsion g…
Elliptic curves with torsion group
A. Dujella, J. C. Peral, P. Tadić
We exhibit several families of elliptic curves with torsion group isomorphic to and generic rank at least . Families of this kind have been constructed previously by s…
Elliptic curves with torsion group Z/8Z or Z/2Z x Z/6Z
Andrej Dujella, Juan Carlos Peral
We show the existence of families of elliptic curves over Q whose generic rank is at least 2 for the torsion groups Z/8Z and Z/2Z x Z/6Z. Also in both cases we prove the existence…
High rank elliptic curves with prescribed torsion group over quadratic fields
Julian Aguirre, Andrej Dujella, Mirela Jukic Bokun +1
There are 26 possibilities for the torsion group of elliptic curves defined over quadratic number fields. We present examples of high rank elliptic curves with given torsion group…
Biquadrates and Elliptic Curves
Julián Aguirre, Juan Carlos Peral
The elliptic curve y^2= x^3-Nx where N=m^4+n^4 has rank at least 2 over Q(m,n). When N can be written in two different ways as sum of two fourth powers, then we prove that the rank…
On the high rank and -congruent number elliptic curves
Ali S. Janfada, Sajad Salami, andrej Dujella +1
Consider the elliptic curves given by where , is rational with and . These e…