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Imaginary quadratic number fields with class groups of small exponent

Volume 193 / 2020

Andreas-Stephan Elsenhans, Jürgen Klüners, Florin Nicolae Acta Arithmetica 193 (2020), 217-233 MSC: Primary 11R29; Secondary 11R11. DOI: 10.4064/aa180220-20-3 Published online: 24 January 2020


Let $D \lt 0$ be a fundamental discriminant and denote by $E(D)$ the exponent of the ideal class group $\operatorname{Cl} (D)$ of $K=\mathbb Q (\sqrt {D})$. Under the assumption that no Siegel zeros exist we compute all such $D$ with $E(D)$ dividing $8$. We compute all $D$ with $|D|\leq 3.1\cdot 10^{20}$ such that $E(D)\leq 8$.


  • Andreas-Stephan ElsenhansUniversität Würzburg
    Campus Hubland Nord
    Emil-Fischer-Str. 30
    97074 Würzburg, Germany
  • Jürgen KlünersInstitut für Mathematik
    Fakultät EIM
    Universität Paderborn
    Warburger Str. 100
    33098 Paderborn, Germany
  • Florin Nicolae“Simion Stoilow” Institute of Mathematics
    of the Romanian Academy
    P.O. Box 1-764
    RO-014700 Bucureşti, Romania

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