Rational torsion generation conjecture for J_1(p)

Let pp be a prime, and let J1(p)J_1(p) be the Jacobian of the modular curve X1(p)X_1(p). A rational cusp difference is a divisor class represented by the difference of two rational cusps. Rational torsion generation conjecture. The rational torsion subgroup of J1(p)J_1(p) is generated by differences of rational cusps.

This is cited as Conjecture 6.2.2 of the referenced source and is used in the discussion of the case =2\ell=2 for X1(p)X_1(p); no resolution is given here.

Sources & referencesView supporting material

Primary source

Maarten Derickx and Michael Stoll, “Prime order torsion on elliptic curves over number fields. Part I: Asymptotics”, arXiv:2505.14109 (2025).

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