Abstract
Let [Formula: see text] be a [Formula: see text]-curve without complex multiplication. We address the problem of deciding whether [Formula: see text] is geometrically isomorphic to a strongly modular [Formula: see text]-curve. We show that the question has a positive answer if and only if [Formula: see text] has a model that is completely defined over an abelian number field. Next, if [Formula: see text] is completely defined over a quadratic or biquadratic number field [Formula: see text], we classify all strongly modular twists of [Formula: see text] over [Formula: see text] in terms of the arithmetic of [Formula: see text]. Moreover, we show how to determine which of these twists come, up to isogeny, from a subfield of [Formula: see text].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
