5 citations · 8 across the 5 of their papers we have counts for
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On the discriminant of elliptic curves with non-trivial torsion
I. Garcia-Selfa, Jose M. Tornero
For those elliptic curves defined over the rational with non--trivial torsion subgroup, we find a tight relationship between the torsion subgroup itself and a Galois group naturall…
Thue equations and torsion groups of elliptic curves
Irene Garcia-Selfa, Jose M. Tornero
A new characterization of rational torsion subgroups of elliptic curves is found, for points of order greater than 4, through the existence of solution for systems of Thue equation…
Searching for simultaneous arithmetic progressions on elliptic curves
Irene Garcia-Selfa, Jose M. Tornero
We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is…
A complete diophantine characterization of the rational torsion of an elliptic curve
Irene Garcia-Selfa, Jose M. Tornero
We give a complete characterization for the rational torsion of an elliptic curve in terms of the (non-)existence of integral solutions of a system of diophantine equations.