Potential Update for Elliptic Curve 5077a1: Rank 4 Subgroup Discovered

[Chris Rice]

Dear LMFDB team,

I would like to report the independent discovery of a rank 4 subgroup of rational points on the elliptic curve 5077a1 over Q. These four generators are linearly independent from the known SageMath basis and verified via canonical height matrix analysis.

The full coordinates, verification scripts, and analysis are published and publicly archived at the following Zenodo DOI: https://doi.org/10.5281/zenodo.15651876

All results were obtained using SageMath and standard canonical height pairing tools, with no conjectural assumptions. Sage's known generators were shown to require non-integer coefficients in the discovered lattice, indicating a distinct subgroup of higher rank.

I invite your team to independently verify the result, and if confirmed, to consider updating the published rank and generator set for 5077a1.

Thank you for maintaining such a valuable resource.

Sincerely,  

Chris Rice  

Independent Researcher  

ORCID: https://orcid.org/0009-0000-0181-3773

[Edgar Costa]

Let Q = [(-2 : 3 : 1), (-1 : 3 : 1), (0 : 2 : 1)]

then P = M*Q where

M =  [

[ -91, -364, -364 ],
[ 188, 282, 0 ],
[ -226, -339, 0 ],
[ 232, 0, -116 ]
]

and thus your 4 points are in the span of Q.

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