On Some Open Cases of a Conjecture of Conrad, Edixhoven and Stein

Let p ≥ 5 be a prime. In 2003 Conrad, Edixhoven, and Stein conjectured that the rational torsion subgroup of the modular Jacobian J 1 (p) coincides with the rational cuspidal divisor class group. Using explicit computations in Magma, the open case p = 29 has been proven by Derickx, Kamienny, Stein, and Stoll in 2023. We extend these results to primes p = 97, 101, 109, and 113. In addition, we provide a list of the groups J 1 (p)(ℚ)tors for every prime up to p ≤ 113. However, our method is general and can be applied to larger primes.