PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
February 21, 2026Forum Mathematicum0 citations

A positive density of elliptic curves is diophantine stable in certain Galois extensions

View Full Paper
ARAnwesh RayPSPratiksha Shingavekar

Key Points

  • Investigate the density of elliptic curves that are diophantine stable over Galois extensions of rational numbers.
  • Consider cyclic p-extension L/Q for p in {3,5}
  • Establish criteria for diophantine stability
  • Analyze elliptic curves ordered by height
  • Demonstrated an effective positive density of diophantine stable elliptic curves.
  • Identified specific elliptic curves defined over Q that meet the stability criteria.

Abstract

Abstract Let p ∈ 3, 5 p\{3, 5\} and consider a cyclic p -extension L / ℚ L/Q. We show that there exists an effective positive density of elliptic curves E defined over ℚ Q, ordered by height, that is diophantine stable in L.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Ray et al. (2026) studied this question.

synapsesocial.com/papers/69994cdf873532290d021cabhttps://doi.org/10.1515/forum-2025-0160
Ask AI
Helpful
Bookmark
Share
View Full Paper

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1The distribution of ℓ^{∞}-Selmer groups in degree ℓ twist families I2025 · 6 citations
  2. 2Rank stability of elliptic curves in certain non‐abelian extensions2025 · 2 citations
  3. 3The average rank of elliptic curves I1992 · 151 citations
  4. 4Ranks of twists of elliptic curves and Hilbert’s tenth problem2010 · 80 citations
  5. 5Advanced Topics in the Arithmetic of Elliptic Curves1994 · 1,681 citations