COMPUTING POINTS ON BIELLIPTIC MODULAR CURVES OVER FIXED QUADRATIC FIELDS

DOI10.1017/s0004972723000333arXiv2301.06440OpenAlexW4366720750MaRDI QIDQ6191811

Philippe Michaud-Jacobs

Publication date: 12 February 2024

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.06440

zbMATH Keywords

elliptic curvemodular curveMordell-Weil sievequadratic point

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Arithmetic aspects of modular and Shimura varieties (11G18)

Cites Work

• The Magma algebra system. I: The user language
• Splitting of primes in number fields generated by points on some modular curves
• Fermat's last theorem over some small real quadratic fields
• Hyperelliptic modular curves and isogenies of elliptic curves over quadratic fields
• Points on quadratic twists of X₀(N)
• AN "ANTI-HASSE PRINCIPLE" FOR PRIME TWISTS
• On quadratic points of classical modular curves
• Fermat’s Last Theorem and modular curves over real quadratic fields
• Quadratic points on modular curves with infinite Mordell–Weil group
• Quadratic points on modular curves
• Quadratic points on bielliptic modular curves
• Cyclic isogenies of elliptic curves over fixed quadratic fields

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