curve #4384

y² = x³ − 92837395950033552980700x + 11530379178598796179215630517096000

a-invariants: [0, 0, 0, -92837395950033552980700, 11530379178598796179215630517096000]
c-invariants: [4456195005601610543073600, -9962247610309359898842304766770944000]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/4ℤ
conductor (N): 7205437693496481352981077600
discriminant (Δ): -6224947956321800094428646916287541945211569366157401151175888960000000
Faltings height: 12.1427
naive height: 170.3837
primes of bad reduction: 2, 3, 5, 31, 37, 43, 79, 257, 263, 3323, 5237, 218357
regulator: 48434881061.691945984679811042814013404209887027788912568
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:20:59 UTC
last updated: 2026-10-17 10:20:59 UTC

(-347348335452070/2209, 15483385310094705933900/103823)
(3624742658627840/41209, 532040277993637029420600/8365427)
(5318566365294786/22801, 174434782413109694756116/3442951)
(198705981829026305/824464, 42049755833271781505118975/748613312)
(2548167484946202365/15311569, 1573216410009811307846172075/59914169497)
(6243541952101899970/16818201, 11588127061894629663072880700/68971442301)
(12262989140149571456/58690921, 15925276226645880458078455704/449631145781)
(13756504304527640330/55905529, 25028941831041821350962563100/418005640333)
(19444379410941125505/30118144, 77647595341119524325939638975/165288374272)

BASE records/family_Z4.md#49 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:20:59 UTC · history