Papers › Good elliptic curves with a specified torsion subgroup
Good elliptic curves with a specified torsion subgroup
Alexander J. Barrios
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An elliptic curve E over ℚ is said to be good if N_E⁶<max{ |c₄³|,c₆²} where N_E is the conductor of E and c₄ and c₆ are the invariants associated to a global minimal model of E. In this article, we generalize Masser's Theorem on the existence of infinitely many good elliptic curves with full $2$-torsion. Specifically, we prove via constructive methods that for each of the fifteen torsion subgroups T allowed by Mazur's Torsion Theorem, there are infinitely many good elliptic curves E with E(ℚ) ₜₒᵣₛ≅T.
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