engleski

A criterion to rule out torsion groups for elliptic curves over number fields

We present a criterion for proving that certain groups of the form Z/mZ+Z/nZ do not occur as the torsion subgroup of any elliptic curve over suitable (families of) number fields. We apply this criterion to eliminate certain groups as torsion groups of elliptic curves over cubic and quartic fields. We also use this criterion to give the list of all torsion groups of elliptic curves occurring over a speci fic cubic fi eld and over a specifi c quartic field.

Elliptic curves ; Torsion

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