Lorenz Halbeisen - Academia.edu (original) (raw)
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Papers by Lorenz Halbeisen
arXiv: Number Theory, Nov 18, 2021
We give new parametrisations of elliptic curves in Weierstrass normal form y 2 = x 3 + ax 2 + bx ... more We give new parametrisations of elliptic curves in Weierstrass normal form y 2 = x 3 + ax 2 + bx with torsion groups Z/10Z and Z/12Z over Q, and with Z/14Z and Z/16Z over quadratic fields. Even though the parametrisations are equivalent to those given by Kubert and Rabarison, respectively, with the new parametrisations we found three infinite families of elliptic curves with torsion group Z/12Z and positive rank. Furthermore, we found elliptic curves with torsion group Z/14Z and rank 3-which is a new record for such curves, as well as some new elliptic curves with torsion group Z/16Z and rank 3.
arXiv: Number Theory, Nov 18, 2021
We give new parametrisations of elliptic curves in Weierstrass normal form y 2 = x 3 + ax 2 + bx ... more We give new parametrisations of elliptic curves in Weierstrass normal form y 2 = x 3 + ax 2 + bx with torsion groups Z/10Z and Z/12Z over Q, and with Z/14Z and Z/16Z over quadratic fields. Even though the parametrisations are equivalent to those given by Kubert and Rabarison, respectively, with the new parametrisations we found three infinite families of elliptic curves with torsion group Z/12Z and positive rank. Furthermore, we found elliptic curves with torsion group Z/14Z and rank 3-which is a new record for such curves, as well as some new elliptic curves with torsion group Z/16Z and rank 3.