We prove that rank-zero elliptic curves over generate positive-rank elliptic curves through the unit circle, via quadratic twisted models . This construction demonstrates rank evolution from zero to infinite rational points, complementing high-rank families. All rank-zero status and positive-rank emergence rigorously verified computationally. SMC(2020): 11G05, 14H52, 11Y50.
| Published in | Pure and Applied Mathematics Journal (Volume 15, Issue 1) |
| DOI | 10.11648/j.pamj.20261501.11 |
| Page(s) | 1-5 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Elliptic Curves, Mordell-Weil Rank, Rank-zero, Congruent Numbers, Rank Lifting, Unit Circle (Parametrizatation)
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APA Style
Vincent, K. K., Fousséni, S. K. (2026). Rank Lifting From Rank-Zero Elliptic Curves Via Quadratic Twists. Pure and Applied Mathematics Journal, 15(1), 1-5. https://doi.org/10.11648/j.pamj.20261501.11
ACS Style
Vincent, K. K.; Fousséni, S. K. Rank Lifting From Rank-Zero Elliptic Curves Via Quadratic Twists. Pure Appl. Math. J. 2026, 15(1), 1-5. doi: 10.11648/j.pamj.20261501.11
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Download@article{10.11648/j.pamj.20261501.11,
author = {Kouakou Kouassi Vincent and Soro Kolo Fousséni},
title = {Rank Lifting From Rank-Zero Elliptic Curves Via Quadratic Twists
},
journal = {Pure and Applied Mathematics Journal},
volume = {15},
number = {1},
pages = {1-5},
doi = {10.11648/j.pamj.20261501.11},
url = {https://doi.org/10.11648/j.pamj.20261501.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20261501.11},
abstract = {We prove that rank-zero elliptic curves over generate positive-rank elliptic curves through the unit circle, via quadratic twisted models . This construction demonstrates rank evolution from zero to infinite rational points, complementing high-rank families. All rank-zero status and positive-rank emergence rigorously verified computationally. SMC(2020): 11G05, 14H52, 11Y50.
},
year = {2026}
}
TY - JOUR T1 - Rank Lifting From Rank-Zero Elliptic Curves Via Quadratic Twists AU - Kouakou Kouassi Vincent AU - Soro Kolo Fousséni Y1 - 2026/01/16 PY - 2026 N1 - https://doi.org/10.11648/j.pamj.20261501.11 DO - 10.11648/j.pamj.20261501.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 1 EP - 5 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20261501.11 AB - We prove that rank-zero elliptic curves over generate positive-rank elliptic curves through the unit circle, via quadratic twisted models . This construction demonstrates rank evolution from zero to infinite rational points, complementing high-rank families. All rank-zero status and positive-rank emergence rigorously verified computationally. SMC(2020): 11G05, 14H52, 11Y50. VL - 15 IS - 1 ER -
Applied Fundamental Sciences Department, Nangui ABROGOUA University, Abidjan, Ivory Coast
Mathematics and Computer Science Department, Alassane Ouattara University, Bouak´e, Ivory Coast
