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math.NT2012★ 11 cited
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…
math.NT2012★ 2 cited
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…