curve #804

y² + xy = x³ − x² − 40608x + 3106480

a-invariants: [1, -1, 0, -40608, 3106480]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 666666
discriminant (Δ): 143999712000144
Faltings height: 1.5093
naive height: 43.4488
primes of bad reduction: 2, 3, 7, 11, 13, 37
regulator: 3.7049951734270990271298804531157317198420187
submitted by: NDElkies
submitted at: 2026-09-19 04:02:04 UTC
last updated: 2026-09-19 04:02:04 UTC

Witness: 3 independent points log in to add more points →

(41, 1208)
(-193, 2027)
(860, 24140)

Commentary

Found in 2012; mostly for numerological fun (alas too late for Curve 666), but with full 2-torsion this curve is not too bad compared with the minimal 174915.b3 .

last edited by NDElkies at 2026-09-19 04:02:04 UTC · history