Class groups of imaginary biquadratic fields

2025/11/06 by Kalyan Banerjee, Banerjee, Kalyan, Kalyan Chakraborty +3
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2511.04529

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

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.

Citations

• Class Number Formulas for Certain Biquadratic Fields
• Quadratic twists of elliptic curves and class numbers

Related

• Class numbers of Imaginary bicyclic biquadratic number fields
• Quadratic fields with a class group of large 3-rank
• Class groups of imaginary quadratic fields of 3-rank at least 2
• Class groups of imaginary quadratic points on X₁(16)
• Notes on the divisibility of the class numbers of certain imaginary quadratic fields