Rational torsion points on Jacobians of modular curves

Hwajong Yoo. "Rational torsion points on Jacobians of modular curves." Acta Arithmetica 172.4 (2016): 299-304. <http://eudml.org/doc/279619>.

@article{HwajongYoo2016,
abstract = {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 $3^\{(p-1)/3\} ≡ 1 (mod p)$.},
author = {Hwajong Yoo},
journal = {Acta Arithmetica},
keywords = {rational points; modular curves; Eisenstein ideals},
language = {eng},
number = {4},
pages = {299-304},
title = {Rational torsion points on Jacobians of modular curves},
url = {http://eudml.org/doc/279619},
volume = {172},
year = {2016},
}

TY - JOUR
AU - Hwajong Yoo
TI - Rational torsion points on Jacobians of modular curves
JO - Acta Arithmetica
PY - 2016
VL - 172
IS - 4
SP - 299
EP - 304
AB - 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 $3^{(p-1)/3} ≡ 1 (mod p)$.
LA - eng
KW - rational points; modular curves; Eisenstein ideals
UR - http://eudml.org/doc/279619
ER -