Thomas C. Martinez

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math.NT2022

Class Numbers and Pell's Equation $x^{2} + 105 y^{2} = z^{2}$

Thomas Jaklitsch, Thomas C. Martinez, Steven J. Miller +1

Two well-studied Diophantine equations are those of Pythagorean triples and elliptic curves, for the first we have a parametrization through rational points on the unit circle, and…

math.NT2020

On Class Numbers, Torsion Subgroups, and Quadratic Twists of Elliptic Curves

Talia Blum, Caroline Choi, Alexandra Hoey +3

The Mordell-Weil groups $E (Q)$ of elliptic curves influence the structures of their quadratic twists $E_{- D} (Q)$ and the ideal class groups $CL (- D)$ of i…

Class Numbers and Pell's Equation x2+105y2=z2

On Class Numbers, Torsion Subgroups, and Quadratic Twists of Elliptic Curves

Class Numbers and Pell's Equation $x^{2} + 105 y^{2} = z^{2}$