ON THE NUMBER OF ELLIPTIC CURVES WITH PRESCRIBED ISOGENY OR TORSION GROUP OVER NUMBER FIELDS OF PRIME DEGREE

DOI10.1017/S0017089514000421zbMath1322.11058arXiv1109.6278OpenAlexW2963580754MaRDI QIDQ5248720

Filip Najman

Publication date: 8 May 2015

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.6278

zbMATH Keywords

elliptic curvesisogenytorsion group

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Arithmetic aspects of modular and Shimura varieties (11G18)

Uses Software

• ecdata

Cites Work

• Unnamed Item
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• Ranks of twists of elliptic curves and Hilbert's tenth problem
• Finiteness theorems for abelian varieties over number fields.
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Modular curves and the Eisenstein ideal
• Defining equations of modular curves
• Galois properties of points of finite order of elliptic curves
• EXCEPTIONAL ELLIPTIC CURVES OVER QUARTIC FIELDS
• On fields of definition of torsion points of elliptic curves with complex multiplication
• Torsion groups of elliptic curves over quadratic fields
• Torsion points on elliptic curves defined over quadratic fields
• On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves
• Constructing elliptic curves over finite fields with prescribed torsion
• ON THE TORSION OF ELLIPTIC CURVES OVER QUARTIC NUMBER FIELDS

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