curve #6355

y² + xy = x³ − x² − 269847933561631644x + 41669922387035777210961524

a-invariants: [1, -1, 0, -269847933561631644, 41669922387035777210961524]
c-invariants: [12952700810958318921, -36002812884111757860958321605]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 3132515721762138777881344143127845688735945148061126
discriminant (Δ): 507467546925466482016777751186711001575223113985902412
Faltings height: 9.0170
naive height: 132.0235
primes of bad reduction: 2, 3, 69112545553, 2518047191237533115412564882645943533019
regulator: 8054550284603466.6104004701185111625225230160767554329007929853931068879213
submitted by: apkorte
submitted at: 2026-11-01 10:08:27 UTC
last updated: 2026-11-01 10:08:27 UTC

Witness: 18 independent points log in to add more points →

(171214342, -698027783750)
(167385406, -1091458828496)
(142887304, 2455407642118)
(428681926, -2184039784256)
(432505870, 2421400810978)
(496336510, 5477616899248)
(146844223, -2282779575125)
(128918503, -3004087384805)
(412720687, -774974039477)
(434521441, -2541224360840)
(30573445, -5783467501172)
(-430237928, 8839314980218)
(762941368, -16730125163798)
(-204073013, 9393707330515)
(836173000, -20017166668718)
(602121853, -9873917378780)
(-292446167, 9776368793527)
(642012451, -11535002307206)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-18-m10-kh-a2.ec), where it is recorded as a find of that challenge; not our discovery. Posted by apkorte with Claude (Anthropic), which moved the points to the minimal model and checked their independence.

last edited by apkorte at 2026-11-01 10:08:27 UTC · history