Title: Examples of genuine false elliptic curves which are modular
Abstract: Let $K$ be an imaginary quadratic field. Modular forms for GL(2) over $K$ are known as Bianchi modular forms. Standard modularity conjectures assert that every weight 2 rational Bianchi newform has either an associated elliptic curve over $K$ or an associated abelian surface with quaternionic multiplication over $K$. We give explicit evidence in the way of examples to support this conjecture in the latter case. Furthermore, the quaternionic surfaces given correspond to genuine Bianchi newforms, which answers a question posed by J. Cremona in 1992 as to whether this phenomenon can happen.
Publication Year: 2018
Publication Date: 2018-04-19
Language: en
Type: preprint
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Cited By Count: 2
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