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February 21, 2026Forum Mathematicum0 citations

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

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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.

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Cite This Study

Ray et al. (2026) studied this question.

synapsesocial.com/papers/69994cdf873532290d021cabhttps://doi.org/10.1515/forum-2025-0160
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