Displaying similar documents to “Rational points on X 0 + ( p ) .”

Rational torsion points on Jacobians of modular curves

Hwajong Yoo (2016)

Acta Arithmetica

Similarity:

Let p be a prime greater than 3. Consider the modular curve X₀(3p) over ℚ and its Jacobian variety J₀(3p) over ℚ. Let (3p) and (3p) be the group of rational torsion points on J₀(3p) and the cuspidal group of J₀(3p), respectively. We prove that the 3-primary subgroups of (3p) and (3p) coincide unless p ≡ 1 (mod 9) and 3 ( p - 1 ) / 3 ≡ 1 ( m o d p ) .