3 citations · 4 across the 4 of their papers we have counts for
4 papers
Rational torsion points on abelian surfaces with quaternionic multiplication
Jef Laga, Ciaran Schembri, Ari Shnidman +1
Let be an abelian surface over whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur's theorem for elliptic cur…
Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves
Oana Padurariu, Ciaran Schembri
Guo and Yang give defining equations for all geometrically hyperelliptic Shimura curves . In this paper we compute the -rational points on the Atkin-Lehner qu…
On rational Bianchi newforms and abelian surfaces with quaternionic multiplication
John Cremona, Lassina Dembélé, Ariel Pacetti +2
We study the rational Bianchi newforms (weight 2, trivial character, with rational Hecke eigenvalues) in the LMFDB that are not associated to elliptic curves, but instead to abelia…
Examples of genuine QM abelian surfaces which are modular
Ciaran Schembri
Let be an imaginary quadratic field. Modular forms for GL(2) over are known as Bianchi modular forms. Standard modularity conjectures assert that every weight 2 rational Bi…