# EC: Why does $h>200$ need to hold?

From BSI-TR-03111 (PDF), on page 15:

The class number of the principal order belonging to the endomorphism ring of E SHOULD be at least 200.

This value commonly is referred to as $h$ in that publication.

I‘ve got two questions related to this:

1. What does $h$ mean/denote?
2. Why should it be 200 or larger?

Don't confuse h which is commonly adopted for the cofactor in EC (Cf p13 of the doc). The class number $\mathcal{H}(K)$ for any number field K is the cardinal of the class group Cl(K). Take a look to any course in algebraic number theory and specially H. COHEN and his famous book " A course in computational Alg. Numb Th ..." The ring theory is very vast, and the link with EC lies in the structure of its endomorphism Ring which can be viewed as an Order in a quadratic field. In H. COHEN you can understand that computing the class number for an random EC is not so easy, this is the reason why this value can't be chosen too small.