Franz's reference reminded me that there is an entire school (Universite Bordeaux I?) of people who study relations between elliptic curves, rings of integers and Galois module structure. It happens that I have hung out a bit with some of these people, but so far they haven't passed on their deep knowledge of this subject (or even their Francophoneness) to me. Nevertheless I found the following interesting paper of Cassou-Noguès and Taylor which came out soon after their book:

Cassou-Noguès, Ph.(F-BORD); Taylor, M. J.(4-UMIST) A note on elliptic curves and the monogeneity of rings of integers. J. London Math. Soc. (2) 37 (1988), no. 1, 63--72.

http://jlms.oxfordjournals.org.proxy-remote.galib.uga.edu/cgi/reprint/s2-37/1/63

I recommend especially the very well written introduction to this paper. It contains the intriguing sentence:

"These results have led us to believe that the rings of integers of all ray class fields of K are monogenic over the ring of integers of the Hilbert class field of K."

Franz's reference reminded me that there is an entire school (Universite Bordeaux I?) of people who study relations between elliptic curves, rings of integers and Galois module structure. It happens that I have hung out a bit with some of these people, but so far they haven't passed on their deep knowledge of this subject (or even their Francophoneness) to me. Nevertheless I found the following interesting paper of Cassou-Noguès and Taylor which came out soon after their book:

Cassou-Noguès, Ph.(F-BORD); Taylor, M. J.(4-UMIST) A note on elliptic curves and the monogeneity of rings of integers. J. London Math. Soc. (2) 37 (1988), no. 1, 63--72.

I recommend especially the very well written introduction to this paper. It contains the intriguing sentence:

"These results have led us to believe that the rings of integers of all ray class fields of K are monogenic over the ring of integers of the Hilbert class field of K."