Premium
The Jacobians of Non‐Split Cartan Modular Curves
Author(s) -
Chen I
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000392
Subject(s) - mathematics , modular design , pure mathematics , algebra over a field , computer science , programming language
The mod p representation associated to an elliptic curve is called split or non‐split dihedral if its image lies in the normaliser of a split or non‐split Cartan subgroup of GL 2 ( f p ), respectively. LetX split +andX non‐split +denote the modular curves which classify elliptic curves with split and non‐split dihedral mod p representation, respectively. We call such curves split and non‐split Cartan modular curves . The curveX split +is isomorphic to the curve X 0 ( p 2 ) . Using the Selberg trace formula for Hecke operators, we verify that the jacobian ofX non‐split +is isogenous to the new part of the jacobian of X 0 ( p 2 ) . 1991 Mathematics Subject Classification : primary 11G18; secondary 11F72.