Open Access
January, 2012 The cuspidal class number formula for the modular curves X1(2p)
Toshikazu TAKAGI
J. Math. Soc. Japan 64(1): 23-85 (January, 2012). DOI: 10.2969/jmsj/06410023


Let p be a prime not equal to 2 or 3. We determine the group of all modular units on the modular curve X1(2p), and its full cuspidal class number. We mention a fact concerning the non-existence of torsion points of order 5 or 7 of elliptic curves over Q of square-free conductor n as an application of a result by Agashe and the cuspidal class number formula for X0(n). We also state the formula for the order of the subgroup of the Q-rational torsion subgroup of J1(2p) generated by the Q-rational cuspidal divisors of degree 0.


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Toshikazu TAKAGI. "The cuspidal class number formula for the modular curves X1(2p)." J. Math. Soc. Japan 64 (1) 23 - 85, January, 2012.


Published: January, 2012
First available in Project Euclid: 26 January 2012

zbMATH: 1277.11068
MathSciNet: MR2879735
Digital Object Identifier: 10.2969/jmsj/06410023

Primary: 11G18
Secondary: 11F03 , 11G05 , 14G05 , 14G35 , 14H40 , 14H52

Keywords: cuspidal class number , Elliptic curve , Jacobian variety , modular curve , modular unit , torsion subgroup

Rights: Copyright © 2012 Mathematical Society of Japan

Vol.64 • No. 1 • January, 2012
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