Splitting of primes in number fields generated by points on some modular curves

DOI10.1007/s40993-022-00325-wOpenAlexW3083470001WikidataQ114218039 ScholiaQ114218039MaRDI QIDQ2138609

Filip Najman, Antonela Trbović

Publication date: 12 May 2022

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.02485

zbMATH Keywords

modular curvesnumber fieldssplitting of primes

Mathematics Subject Classification ID

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

Related Items (3)

Cyclic isogenies of elliptic curves over fixed quadratic fields ⋮ COMPUTING POINTS ON BIELLIPTIC MODULAR CURVES OVER FIXED QUADRATIC FIELDS ⋮ Tamagawa numbers of elliptic curves with prescribed torsion subgroup or isogeny

Uses Software

• Magma

Cites Work

• Unnamed Item
• Galois properties of torsion points on abelian varieties
• Modular curves and the Eisenstein ideal
• The Magma algebra system. I: The user language
• Two theorems on modular curves
• Ranks of Elliptic Curves with Prescribed Torsion over Number Fields
• Hyperelliptic modular curves and isogenies of elliptic curves over quadratic fields
• Points on quadratic twists of X₀(N)
• On the j -Invariants of the Quadratic Q -Curves
• Galois groups via Atkin-Lehner twists
• p-Torsion points on elliptic curves defined over quadratic fields
• Torsion points on elliptic curves defined over quadratic fields
• Fields of definition of elliptic curves with prescribed torsion
• Quadratic points on modular curves with infinite Mordell–Weil group
• Tamagawa Numbers of elliptic curves with 𝐶₁₃ torsion over quadratic fields

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