## Speaker:

Wenhan Wang

## Institution:

University of Washington

## Time:

Tuesday, February 5, 2013 - 2:00pm to 3:00pm

## Host:

## Location:

RH306

The endomorphism rings of ordinary jacobians of genus two curves defined over finite

fields are orders in quartic CM fields. The conductor gap between two endomorphism rings is

defined as the largest prime number that divides the conductor of one endomorphism ring but not

the other. We call a genus two curve isolated, if its endomorphism ring has large conductor gap

(>=80 bits) with any other possible endomorphism rings. There is no known algorithm to explicitly

construct isogenies from an isolated curve to curves in other endomorphism classes. I will

explain results on criteria for a curve to be isolated, as well as the heuristic asymptotic

distribution of isolated genus two curves.