Torsion of elliptic curves with rational 𝑗-invariant defined over number fields of prime degree | Zendy

Tomislav Gužvić | Zendy

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Torsion of elliptic curves with rational 𝑗-invariant defined over number fields of prime degree

Author(s) -

Tomislav Gužvić

Publication year - 2021

Publication title -

proceedings of the american mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.968

H-Index - 84

eISSN - 1088-6826

pISSN - 0002-9939

DOI - 10.1090/proc/15500

Subject(s) - mathematics , schoof's algorithm , elliptic curve , pure mathematics , torsion (gastropod) , modular elliptic curve , invariant (physics) , discrete mathematics , quarter period , mathematical physics , medicine , surgery

Let [ K : Q ] = p [K:\mathbb {Q}]=p be a prime number and let E / K E/K be an elliptic curve with j ( E ) ∈ Q j(E) \in \mathbb {Q} . We determine the all possibilities for E ( K ) t o r s E(K)_{tors} . We obtain these results by studying Galois representations of E E and of its quadratic twists.

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