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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)(\\mathbb{Q})_{\\text{tors}} \\) for every prime up to \\( p \\leq 113 \\). 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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)(\\mathbb{Q})_{\\text{tors}} \\) for every prime up to \\( p \\leq 113 \\). 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