engleski

Torsion points on rational elliptic curves over the compositum of all cubic fields

Let E/Q be an elliptic curve and let Q(3∞) be the compositum of all cubic extensions of Q. In this article we show that the torsion subgroup of E(Q(3∞)) is finite and determine 20 possibilities for its structure, along with a complete description of the Q-isomorphism classes of elliptic curves that fall into each case. We provide rational parameterizations for each of the 16 torsion structures that occur for infinitely many Q-isomorphism classes of elliptic curves, and a complete list of j-invariants for each of the 4 that do not.

elliptic curves ; torsion

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