Modular Abelian Varieties of Odd Modular Degree

Details Modular Abelian Varieties of Odd Modular Degree Modular Abelian Varieties of Odd Modular Degree

2009-10-03

arxiv.org/abs/0910.0571v1

Mathematics

Number Theory

22 pages, submitted to Math Annalen

Scientific paper

In this paper, we will study modular Abelian varieties with odd congruence numbers by examining the cuspidal subgroup of $J_0(N)$. We will show that the conductor of such Abelian varieties must be of a special type. For example, if $N$ is the conductor of an absolutely simple modular Abelian variety with an odd congruence number, then $N$ has at most two prime divisors, and if $N$ is odd, then $N=p^\alpha$ or $N=pq$ for some prime $p$ and $q$. In the second half of this paper, we will focus on modular elliptic curves with odd modular degree. Our results, combined with the work of Agashe, Ribet, and Stein, finds necessary condition for elliptic curves to have odd modular degree. In the process we prove Watkins's conjecture for elliptic curves with odd modular degree and a nontrivial rational torsion point.

Affiliated with

Also associated with

No associations

Rating

Modular Abelian Varieties of Odd Modular Degree does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Modular Abelian Varieties of Odd Modular Degree, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modular Abelian Varieties of Odd Modular Degree will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-664908