The cuspidal class number formula for the modular curves X-1(2p)
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN(2012)
Abstract
Let p be a prime not equal to 2 or 3. We determine the group of all modular units on the modular curve X-1 (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 X-0(n). We also state the formula for the order of the subgroup of the Q-rational torsion subgroup of J(1)(2p) generated by the Q-rational cuspidal divisors of degree 0.
MoreTranslated text
Key words
modular curve,modular unit,cuspidal class number,elliptic curve,Jacobian variety,torsion subgroup
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined