Imaginary biquadratic number fields with small odd class numbers
Abstract
An imaginary biquadratic field $K$ is a number field of the form $\mathbf{Q}(\sqrt{-m_{1}}, \sqrt{-m_{2}})$, where $m_{1}$ and $m_{2}$ are distinct positive squarefree integers. In this paper, we present an algorithm for determining all the imaginary biquadratic fields with small odd class numbers. We use this algorithm to determine all imaginary biquadratic fields $K$ with odd class number $h(K)$ satisfying $1\leq h(K)< 50$. Moreover, we note that many of these fields are not found in the L-functions and modular forms database (LMFDB) as of writing.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Mathematical Identities
Analytic Number Theory Research
Publication details
- Journal / source
- Proceedings of the Japan Academy Series A Mathematical Sciences
- Volume
- 102
- Issue
- 1
- Publication date
- 1 January 2026