curve #1109

y² + xy = x³ − 656566580528041526076907434779x + 204763686511453405853594537484357296391508689

a-invariants: [1, 0, 0, -656566580528041526076907434779, 204763686511453405853594537484357296391508689]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1286799043897115641009631514
discriminant (Δ): 1112228025484236676570331418931289835048770897052666916176534438963354782161972252114944
Faltings height: 15.7920
naive height: 217.5841
primes of bad reduction: 2, 3, 7, 11, 13, 17, 29, 31, 41, 47, 53, 61, 113, 193, 281, 599, 613
regulator: 405796.892122181674849267535054488783586908307747047466
submitted by: dujella
submitted at: 2026-09-23 20:13:35 UTC
last updated: 2026-09-23 20:13:35 UTC

(50900064512542, 13094895084332895785329)
(311089955373442, 5533421800790073001189)
(334153933123486, 4762417864510138878577)
(365015487014878, 3706754651255271985201)
(-371832437144672, -19937078913637958859689)
(-70309868476526, -15829694250402987332231)
(469950833947294, 9772969417713770737)
(464505611873086, 95361784093264808497)

found by Dujella - Peral (2016)

last edited by dujella at 2026-09-23 20:13:36 UTC · history