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Fields of definition of elliptic curves with prescribed torsion (CROSBI ID 247237)
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Bruin, Peter ; Najman, Filip
Fields of definition of elliptic curves with prescribed torsion // Acta Arithmetica, 181 (2017), 1; 85-96. doi: 10.4064/aa170323-20-9
Podaci o odgovornosti
Bruin, Peter ; Najman, Filip
engleski
Fields of definition of elliptic curves with prescribed torsion
We prove that all elliptic curves over quadratic fields with a subgroup isomorphic to C16, as well as all elliptic curves over cubic fields with a subgroup isomorphic to C2 × C14, are base changes of elliptic curves defined over Q. We obtain these results by studying geometric properties of modular curves and maps between modular curves, and then obtaining a modular description of these curves and maps.
elliptic curves ; torsion
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