Class groups of imaginary biquadratic fields
Number Theory
2025-11-07 v1
Abstract
We present two distinct families of imaginary biquadratic fields, each of which contains infinitely many members, with each member having large class groups. Construction of the first family involves elliptic curves and their quadratic twists, whereas to find the other family, we use a combination of elliptic and hyperelliptic curves. Two main results are used, one from Soleng and the other from Banerjee and Hoque.
Cite
@article{arxiv.2511.04529,
title = {Class groups of imaginary biquadratic fields},
author = {Kalyan Banerjee and Kalyan Chakraborty and Arkabrata Ghosh},
journal= {arXiv preprint arXiv:2511.04529},
year = {2025}
}
Comments
9 pages, accepted for publication in "Research in Number Theory"