A generalised Weber function is given by , where η(z) is the Dedekind function and N is any integer; the original function corresponds to N=2. We classify the cases where some power evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating and j(z). Our ultimate goal is the use of these invariants in constructing reductions of elliptic curves over finite fields suitable for cryptographic use.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-4-1,
author = {Andreas Enge and Fran\c cois Morain},
title = {Generalised Weber functions},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {309-341},
zbl = {1319.11039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-4-1}
}
Andreas Enge; François Morain. Generalised Weber functions. Acta Arithmetica, Tome 166 (2014) pp. 309-341. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-4-1/