● Covered by 1 source · 1 reportLow impact1 neutral
Elliptic Curve with Rank ≥ 30 Discovered
Key points
- Curve #273 has been identified.
- It demonstrates a rank of at least 30.
- The discovery includes 30 independent points as witness.
- High-rank elliptic curves are rare in mathematics.
Discovery of Curve #273
An elliptic curve, designated as #273, has been discovered. This curve is defined by the equation y^2 + xy = x^3 − 201769035260418549083594900060734240952308696994802735114305555x + 1151107939141058565733479426024323225135665982951300586808823640527729578307228357301072889377.
Rank of the Curve
The curve has been shown to possess a rank of at least 30. This rank is evidenced by the provision of 30 independent points that lie on the curve. These points serve as a witness to the curve's high rank.
Significance for Number Theory
The discovery of an elliptic curve with such a high rank is notable within the field of number theory. Elliptic curves with high ranks are uncommon and are of particular interest to mathematicians studying the Birch and Swinnerton-Dyer conjecture, one of the Millennium Prize Problems. Such findings contribute to the ongoing research and understanding of these complex mathematical objects.
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Reporting from
A new elliptic curve, identified as #273, has been found to have a rank of at least 30. This discovery is significant for number theorists working on the Birch and Swinnerton-Dyer conjecture, as high-rank curves are rare and provide valuable data for research.