Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 23 min ago
PreprintCC BY 4.0arXiv

Models of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-Isogeny

  • Roberto Hernandez
Open at sourcePDFDOICite

Abstract

Let E be a non-CM elliptic curve defined over ℚ. We present models of curves that have 2-adic image as large as possible, given the constraint that they have a rational 2-isogeny. These curves are known to be generic, and one of the aims of this article is to make that fact explicit. Our techniques make use of modular curves and their j-maps, as well as classification results on isogeny-graphs that have appeared in the literature recently.

Related

  1. Experiments on $3$-isogeny Selmer groups of elliptic curves with a $3$-torsion point
    Ariel Weiss, Dongchen Zou
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. On the elliptic regularization of maximal slope curves
    Massimo Gobbino, Filippo Quattrocchi
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXivHAL
  3. On Greenberg's conjecture for rational elliptic curves at Eisenstein primes
    Zichao Lin, Mulun Yin
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Maximal singular curves over finite fields from elliptic and hyperelliptic curves
    Cesar Hilario, Rodrigo Salomão, Renato Vidal Martins
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Ideal Classes of Order 2n in a Family of Totally Real Cubic Fields and Rational Points on Associated Elliptic Curves
    Junyu Lu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{hernandez2026models,
  title = {{Models of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-Isogeny}},
  author = {Roberto Hernandez},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09509},
  eprint = {2609.09509},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09509},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Models of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-Isogeny
AU  - Roberto Hernandez
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.09509
UR  - https://arxiv.org/abs/2609.09509
AB  - Let E be a non-CM elliptic curve defined over ℚ. We present models of curves that have 2-adic image as large as possible, given the constraint that they have a rational 2-isogeny. These curves are known to be generic, and one of the aims of this article is to make that fact explicit. Our techniques make use of modular curves and their j-maps, as well as classification results on isogeny-graphs that have appeared in the literature recently.
ER  -