Tohoku Mathematical Journal
2026
June
SECOND SERIES VOL. 78, NO. 2

Tohoku Math. J.
78 (2026), 291-310

Title TORSION OF ELLIPTIC CURVES WITH RATIONAL $j$-INVARIANT OVER THE MAXIMAL ELEMENTARY ABELIAN 2-EXTENSION OF \mathbb{Q}

Author Lucas Hamada

(Received December 16, 2024, revised February 7, 2025)
Abstract. In this paper, we classify the possible torsion subgroup structures of elliptic curves defined over the compositum of all quadratic extensions of the rational number field, whose $j$-invariant is a rational number not equal to 0 or 1728.

Mathematics Subject Classification. Primary 11G05; Secondary 12F05.
Key words and phrases. Elliptic curves, torsion points, number fields.

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