curve #4387

y² = x³ + x² + 16690122974038937459060695x + 34890403025633071183889482455263070600

a-invariants: [0, 1, 0, 16690122974038937459060695, 34890403025633071183889482455263070600]
c-invariants: [-801125902753868998034913344, -30145308214142166747463989627359083518304]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 138069388263663287852601180
discriminant (Δ): -823440037278438075350232695074884466698313137314473218429368899284567931566000
Faltings height: 13.6358
naive height: 186.4137
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 37, 41, 53, 71, 163, 173, 18913, 44417
regulator: 86698449542.0044644547145639217773606753594150896821160
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:11 UTC
last updated: 2026-10-17 10:21:11 UTC

(167107345714205545/177241, 535302948409532698655254995/74618461)
(2582598213575772745/234256, 4476530788747889598058860045/113379904)
(5900865647019372403825/853107264, 546634958366776869242769101840855/24917556966912)
(594509515020553/256, 38023216934127822171621/4096)
(-2483702019990191918775/1409777209, 7106804680506024050337233005245/52932904866323)
(290215961345383268437033/117238444801, 383722942799529761928190450707596319/40142560738307201)
(256672576552322920604065/3081027049, 130197864671933076215101234316271285/171018568408843)
(15432709512562695009303625/745409483641, 61912466404845542519773735353447454365/643564931300613811)

2-ISOG#1 dujella/z6old678.html#pre123 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:12 UTC · history