Research Article
Rank Lifting From Rank-Zero Elliptic Curves Via Quadratic Twists
Kouakou Kouassi Vincent*,
Soro Kolo Fousséni
Issue:
Volume 15, Issue 1, February 2026
Pages:
1-5
Received:
30 November 2025
Accepted:
7 January 2026
Published:
16 January 2026
DOI:
10.11648/j.pamj.20261501.11
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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.
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(2...
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