Chris RiceUPDATE: Canonical summation finds rational points on elliptic curve 5077a1
We discovered four rational points on 5077a1 using a canonical summation toolset. These were originally believed to be independent generators, but have since been confirmed to lie in the
𝑍-span of Sage’s known basis.
All four points remain valid and were found independently, without descent or modular methods. A formal correction notice and updated documentation are now included.
Preprint + correction + dataset:
https://doi.org/10.5281/zenodo.15651876
Comments, verification, and feedback still welcome!
Discovery of a Rank 4 Subgroup on Elliptic Curve 5077a1 via Canonical Height Analysis
We present the discovery of four independent rational points on the elliptic curve 5077a1 over Q, forming a full-rank subgroup of rank 4. This exceeds the currently published rank 3 in both the LMFDB and Cremona tables. The result was obtained via a canonical height–driven generator-hunting algorithm that validates linear independence through the canonical height pairing matrix. We provide the exact coordinates of all four generators and confirm that they span a subgroup of strictly higher rank than the SageMath default basis. All data, verification scripts, and rational point files are publicly archived for independent validation.
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