On ideal class groups and units in terms of the quadratic form x2+32y2

For quadratic number fields F = Q(root 2p(1)...p(t-1)) with primes p(j) = 1 mod 8, the authors study the class number and the norm of the fundamental unit of F. The results generalize nicely what has been familiar for the fields Q(root/2-p) with a prime p = 1 mod 8, including density statements. And the results are stated in terms of the quadratic form x(2) + 32y(2) and illustrated in terms of graphs.