The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions. I

DOI10.1007/s40993-023-00456-8arXiv2301.09176MaRDI QIDQ6175164

Nathan Kaplan, John Cullinan

Publication date: 21 July 2023

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

Full work available at URL: https://arxiv.org/abs/2301.09176

zbMATH Keywords

Mordell-Weil groupFrobenius endomorphismanomalous pairisogeneous elliptic curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Curves over finite and local fields (11G20) Varieties over finite and local fields (11G25)

Related Items (1)

The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions. I

Cites Work

• On the number of Q-isomorphism classes of elliptic curves in each Q- isogeny class
• The Magma algebra system. I: The user language
• On the 2-adic valuation of the cardinality of elliptic curves over finite extensions of \(\mathbb{F}_{q}\)
• A remark on the group structure of elliptic curves in towers of finite fields
• Complex multiplication structure of elliptic curves
• Elliptic curves over \(\mathbb {Q}\) and 2-adic images of Galois
• Infinite families of isogeny-torsion graphs
• Galois representations attached to elliptic curves with complex multiplication
• A remark on the group structure of 2-isogenous elliptic curves in towers of finite fields
• Elliptic curves with isomorphic groups of points over finite field extensions
• An algorithm to compute volcanoes of 2-isogenies of elliptic curves over finite fields
• QUOTIENTS OF ELLIPTIC CURVES OVER FINITE FIELDS
• Mathematics of Public Key Cryptography
• Isogeny volcanoes
• The image of Galois representations attached to elliptic curves with an isogeny
• Computing endomorphism rings of Jacobians of genus 2 curves over finite fields
• The Arithmetic of Elliptic Curves
• A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves
• The decomposition of primes in torsion point fields
• Group structure of elliptic curves over finite fields.
• The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions. I

This page was built for publication: The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions. I