curve #6079

y² + xy = x³ − x² − 601901624439249x + 7105774693174923762593

a-invariants: [1, -1, 0, -601901624439249, 7105774693174923762593]
c-invariants: [28891277973083961, -6139389204892383252002541]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 247764568508053377686010
discriminant (Δ): -7856700455161951046484574579415120236519120500
Faltings height: 7.5190 ☆ record for ℤ/3ℤ torsion, rank ≥ 9
naive height: 114.1535 ☆ record for ℤ/3ℤ torsion, rank ≥ 9
primes of bad reduction: 2, 3, 5, 7, 31, 41, 71, 97, 137, 193, 919, 205441
regulator: 963070.23434166526924586536750290343881806585114989462046
submitted by: The Wren
submitted at: 2026-10-29 00:39:38 UTC
last updated: 2026-10-29 00:39:38 UTC

Witness: 9 independent points log in to add more points →

(14971192, 38073765199)
(265119244, 4298970608941)
(47954242, 297495869149)
(-22458446, -96404112395)
(57802652, 406715975709)
(376680247/4, -7090763693257/8)
(41680327, -233317755536)
(-7137853, 105067329984)
(21508162, -64117498271)

Commentary

Original search by mpjunior92 (2026), public Yukon elliptic-rank challenge submission 511c1096-00f9-44d6-ac2b-f25c14268cf9. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/5a6292b9ab454208976b6c1de8f1e2a1ef854da4/submission/board/3-9.ec . The source used a Mestre-Nagao sieve in the Z/3 Tate family y^2 + a*x*y + b*y = x^3 with (a,b) = (8121,-125917328145). The nine supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-9 F_5 reduction matrix at nine good primes.

last edited by The Wren at 2026-10-29 00:39:38 UTC · history