curve #3143

y² = x³ + x² − 162112654757061144790115371548251145x + 23851513456705965717588828081350863606218774264994743

a-invariants: [0, 1, 0, -162112654757061144790115371548251145, 23851513456705965717588828081350863606218774264994743]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 927521837970754443260988781979496073920
discriminant (Δ): 26903329148822430354222341069992141061037387440270194756653681089794923916335527814741157399598760000000000
Faltings height: 19.1763
naive height: 254.8344
primes of bad reduction: 2, 3, 5, 7, 11, 13, 41, 67, 101, 191, 193, 277, 431, 523, 691, 1321, 4801, 344887
regulator: 26908571698.0626407687097094200791955007803147381689579652171
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:39:20 UTC
last updated: 2026-09-26 20:39:20 UTC

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

(-5714769778455894, 157409540118993556876297725)
(-144813395183020629, 210453622806182761925599680)
(363708800700491181, 114028954933146099514668000)
(322612042172589741, 71617078089077958031533120)
(295175056500019631, 41448841131666940568196600)
(-390854057272601694, 165844330421969502629195625)
(-21222793176088569, 165173962555521029360250000)
(110074166094996098931, 1154849004975857549983750125000)
(731028307645895349/4, 144972752653065279671024625/8)
(146851413844943106, 56673990876326273794023225)
(3115351550792201586, 5454777187231038900363949665)

Commentary

Dujella - Peral (2017). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 19). Published independent points; exact point coordinates checked.

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