N. Hungerbuhler

activity

20152025

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4 papers · 1 filter

math.NT2025

Integer triangles with a rational ratio of circumcircle radius to excircle radius

Lorenz Halbeisen, Norbert Hungerbühler, Arman Shamsi Zargar

We consider the problem of finding integer triangles with $R / r$ a positive rational, where $R$ and $r$ are the radii of the circumcircle and an excircle, respectively. We show that…

math.NT2021

A geometric approach to elliptic curves with torsion groups $Z /10 Z$ , $Z /12 Z$ , $Z /14 Z$ , and $Z /16 Z$

Lorenz Halbeisen, Norbert Hungerbuehler, Maksym Voznyy +1

We give new parametrisations of elliptic curves in Weierstrass normal form $y^{2} = x^{3} + a x^{2} + b x$ with torsion groups $Z /10 Z$ and $Z /12 Z$ over $\math…

math.NT2018

Congruent number elliptic curves with rank at least two

Lorenz Halbeisen, Norbert Hungerbühler

We give an infinite family of congruent number elliptic curves, each with rank at least two, which are related to integral solutions of $m^{2} = n^{2} + n l + l^{2}$ .