Number Theory Seminar

We prove a level raising mod p=2 theorem for elliptic curves over Q,
generalizing theorems of Ribet and Diamond-Taylor. As an application, we
show that the 2-Selmer rank can be arbitrary in level raising families. We
will begin by explaining our motivation from W. Zhang's approach to the
p-part of the BSD conjecture. Explicit examples will be given to
illustrate different phenomena compared to odd p. This is joint work with
Bao V. Le Hung.