Abstract
In this paper, we obtain some non-congruent numbers by studying the 8-ranks of the class groups of imaginary quadratic number fields \(\mathbb {Q}(\sqrt{-n})\) and the homogeneous spaces of congruent elliptic curves \(E_{n}\). We also give some criteria for non-congruent numbers in terms of class groups.
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The authors would like to thank the referee for many useful suggestions.
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This research is supported by NSFC (Nos. 12231009, 11971224, 12071209).
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Li, G., Qin, H. Diophantine equations, class groups and non-congruent numbers. Ramanujan J 62, 1081–1105 (2023). https://doi.org/10.1007/s11139-023-00742-0
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DOI: https://doi.org/10.1007/s11139-023-00742-0