$J_1\left(p\right)$ has connected fibers.

Conrad, Brian, Edixhoven, Bas, and Stein, William. " has connected fibers.." Documenta Mathematica 8 (2003): 331-408. <http://eudml.org/doc/126737>.

@article{Conrad2003,
author = {Conrad, Brian, Edixhoven, Bas, Stein, William},
journal = {Documenta Mathematica},
keywords = {Jacobians of modular curves; component groups; resolution of singularities},
language = {eng},
pages = {331-408},
publisher = {Universiät Bielefeld, Fakultät für Mathematik},
title = { has connected fibers.},
url = {http://eudml.org/doc/126737},
volume = {8},
year = {2003},
}

TY - JOUR
AU - Conrad, Brian
AU - Edixhoven, Bas
AU - Stein, William
TI - has connected fibers.
JO - Documenta Mathematica
PY - 2003
PB - Universiät Bielefeld, Fakultät für Mathematik
VL - 8
SP - 331
EP - 408
LA - eng
KW - Jacobians of modular curves; component groups; resolution of singularities
UR - http://eudml.org/doc/126737
ER -