Elliptic curves over imaginary biquadratic number fields of class number one

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Published: 2025-01-15
DOI: https://doi.org/10.56947/gjom.v19i1.2430
Keywords:
Elliptic curves, imaginary biquadratic number fields, hyperelliptic curves

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Zakariae Cheddour
Department of Mathematics, University Abdelmalek Essaadi, Faculty of Sciences and Technology Al Hoceima, Morocco
Abdelhakim Chillali
Department of Mathematics, University of Sidi Mohamed Ben Abdellah-USMBA, FP Taza, LSI Laboratory, Morocco
Ali Mouhib
Department of Mathematics, University of Sidi Mohamed Ben Abdellah-USMBA, FP Taza, LSI Laboratory, Morocco

Abstract

This research investigates elliptic curves within an imaginary biquadratic number field ℵ of class number one. Our study focuses on the existence of torsion subgroups isomorphic to G11, G13, G14, G15, G16, G18, G2 ⊕ G10, and G2 ⊕ G12 over ℵ.

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Issue

Vol. 19 No. 1 (2025)

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Articles

How to Cite

Elliptic curves over imaginary biquadratic number fields of class number one. (2025). Gulf Journal of Mathematics, 19(1), 75-92. https://doi.org/10.56947/gjom.v19i1.2430