Confirm Goldfeld Conjectured for Infinitely Many Elliptic Curves
Safwan Aouira1, Hasan Sankari2, Ahmad Abdo3
1Dr. Safwan Aouira, Professor, Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.
2Dr. Hasan Sankari, Professor, Department of Mathematics, Faculty of Science, Lattakia University, Lattakia, Syria.
3Ahmad Abdo, Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.
Manuscript received on 08 December 2025 | First Revised Manuscript received on 13 December 2025 | Second Revised Manuscript received on 17 March 2026 | Manuscript Accepted on 15 April 2026 | Manuscript published on 30 April 2026 | PP: 3-4 | Volume-6 Issue-1, April 2026 | Retrieval Number: 100.1/ijam.A123006010426 | DOI: 10.54105/ijam.A1230.06010426
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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.
Keywords: Elliptic Curves, Goldfeld Conjectured, Analytic Rank, Optimal Elliptic Curve, Modular Curve and Binary Goldbach Problem.
Scope of the Article: Number Theory