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<p>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 [<CitationRef CitationID="CR13">13</CitationRef>] and the other from Banerjee and Hoque [<CitationRef CitationID="CR3">3</CitationRef>].</p>

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Class groups of imaginary biquadratic fields

  • 期刊论文

  • 发表日期：

    2025年11月16日

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  • Kalyan Banerjee,
  • Kalyan Chakraborty,
  • Arkabrata Ghosh

摘要

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 [13] and the other from Banerjee and Hoque [3].