curve #6371

y² + xy = x³ + x² − 87767985943430902x + 14099201872415146640041480

a-invariants: [1, 1, 0, -87767985943430902, 14099201872415146640041480]
c-invariants: [4212863325284683321, -12181710449363161636630963565]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 165139730720856957117506153800889492719508461714386
discriminant (Δ): -42606050525981094936316587680629489121633183122311588
Faltings height: 8.8017
naive height: 129.3395
primes of bad reduction: 2, 3, 43, 7433, 18523, 828520499779057, 5611166402062169654413859
regulator: 3969749013831059.4277821765924998864793925275480365987641754559162341551267
submitted by: The Wren
submitted at: 2026-11-01 19:40:19 UTC
last updated: 2026-11-01 19:40:19 UTC

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

(416319946, 7050832077490)
(-86398601, 4586685965614)
(-88134941, -4598870629061)
(-166596138, -4908812166064)
(251583549, -2818284887413)
(-282498166, -4043207672398)
(135431572, 2167117624756)
(199913908, 2131292606980)
(99527062, 2519829392602)
(-84185276, 4570746570364)
(1716069535/4, 59547737800355/8)
(207270907, 2193538256842)
(73432615, 2837240753755)
(-213571388, 4806597895936)
(-225673004, -4734116082860)
(-274642994, 4182012503320)
(22162238, -3487840232728)
(6772164, -3674936482628)

Commentary

From Layr-Labs/elliptic-rank-challenge-public, submission/board/1-18-m10-a.ec, commit debf8f35561f00231e8c084c95b7d4e68337de78. The public file contains 18 rational points on the displayed generalized Weierstrass model. All 18 points were rechecked exactly. The minimal discriminant is -42606050525981094936316587680629489121633183122311588. The conductor is 165139730720856957117506153800889492719508461714386. Naive height is 129.33946638848735. Source attribution remains with Layr-Labs.

last edited by The Wren at 2026-11-01 19:40:20 UTC · history