Curve #273 is a notable entry on the Elliptic Curve Rank Leaderboard, featuring a rank lower bound of 30. The curve is defined by the equation y2 + xy = x3 − 201769035260418549083594900060734240952308696994802735114305555x + 1151107939141058565733479426024323225135665982951300586808823640527729578307228357301072889377. It has a conductor N of 2381958488309327728488641214562148525681586925734398576894288277390640894675828305511266759053188773997283310012808983216600083938367948090232306090, making it a record holder for curves with rank ≥ 30. The naive height is recorded at 442.0854, and the Faltings height stands at 34.7705, both also records for this rank category. The discriminant Δ is an extremely large negative number: -46714661255308767314567688733841531918983356002159772613256840842851650254036518701100578342601553513579222272710220496887616034526983492843954090554197033638137245037791044053017600000000. The primes of bad reduction include 2, 3, 5, 7, 13, 31, 41, 47, 53, 67, 379, 4349, 25721454817, 97018222656318846556561979214040553412450110580812087282349817173780902099339117104673990259247421230916714670243202937. The regulator is approximately 10720686604115654188358042985326663938.588084900092986474567459949780498792191278825612795832355129. This curve was submitted by user ranksunbounded on 2026-08-20 and includes a witness set of 30 independent points.

The curve's invariants and properties make it significant in the study of elliptic curves, particularly those with high ranks. Its submission to the leaderboard highlights ongoing research into finding curves with increasing rank values. The data provided includes a comprehensive list of 30 independent points that serve as a witness to the rank lower bound.

Researchers and enthusiasts can access the curve's data in JSON format, contributing to collaborative efforts in computational number theory. The entries on the leaderboard, including curve #273, are regularly updated to reflect new discoveries and improvements in the field.