Confirm Goldfeld Conjectured for Infinitely Many Elliptic Curves

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Published: 30-04-2026
DOI: https://doi.org/10.54105/ijam.A1230.06010426
Keywords:
Elliptic Curves, Goldfeld Conjectured, Analytic Rank, Optimal Elliptic Curve, Modular Curve and Binary Goldbach Problem

Main Article Content

Dr. Safwan Aouira
Professor, Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.
Dr. Hasan Sankari
Professor, Department of Mathematics, Faculty of Science, Lattakia University, Lattakia, Syria.
Ahmad Abdo
Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.
https://orcid.org/0000-0002-1333-3619

Abstract

Goldfeld conjectured: "a positive proportion of quadratic twists of an elliptic curve E/Q have an analytic rank of 1. In this work, we confirm this assertion for infinitely many elliptic curves.

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Vol. 6 No. 1 (2026): Volume-6 Issue-1, April 2026

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

CC-BY-NC-ND 4.0

Author Biography

Ahmad Abdo, Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.



How to Cite

[1]
Dr. Safwan Aouira, Dr. Hasan Sankari, and Ahmad Abdo , Trans., “Confirm Goldfeld Conjectured for Infinitely Many Elliptic Curves”, IJAM, vol. 6, no. 1, pp. 3–4, Apr. 2026, doi: 10.54105/ijam.A1230.06010426.
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