curve #3144

y² = x³ − x² − 1195364158708632186420472502166033x + 15823209428289198577068263787846917629174435793937

a-invariants: [0, -1, 0, -1195364158708632186420472502166033, 15823209428289198577068263787846917629174435793937]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1147380349855782426890573749991101411819200
discriminant (Δ): 1153678499379820937529225221052787403439927022911153392821510398448416497883931371807474489600000000
Faltings height: 17.8469
naive height: 240.1049
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 29, 47, 89, 101, 103, 109, 139, 197, 677, 881, 1283, 1289, 15307
regulator: 7863402754.08206912644241703484426200834646734369165549707229
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:39:24 UTC
last updated: 2026-09-26 20:39:24 UTC

Witness: 11 independent points log in to add more points →

(21349740897066721, 184256415571566123151392)
(27842727329378481, 2031053815354352993276688)
(18187882712729337, 314008176732366060450000)
(-3850615432050288, 4513203198243227693757375)
(47937121011972327, 8287269914001253525673400)
(12616722517196937, 1658307180987975960468000)
(-14755980954997273, 5499911638908231286651000)
(18728393648724587, 70668848553905017916500)
(12571749389540168, 1668035293552115577188099)
(-4259751744481813, 4564851446386533671220500)
(16213801932188337, 839175500122668603414000)

Commentary

Dujella - Peral (2019). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 25). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:39:24 UTC · history