curve #4619

y² = x³ + x² − 1183655708893145385780753788258736251600x + 54390988302913059979704969863573645763089883384478627462500

a-invariants: [0, 1, 0, -1183655708893145385780753788258736251600, 54390988302913059979704969863573645763089883384478627462500]
c-invariants: [56815474026870978517476181836419340076816, -46993813893716883822805986806288855810414516335208050168060864]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 186851261265189445749370728121637790157167538096392355786258939802312387760
discriminant (Δ): -1171885591839538001305644365165167587174171890426516649462023091987886831348217921760849820774106709689194362116192640000
Faltings height: 21.7226
naive height: 284.0102
primes of bad reduction: 2, 3, 5, 11, 113, 139, 163, 167, 233, 239, 241, 353, 653, 797, 977, 1013, 1217, 1657, 3767, 12373, 18481, 42061, 123113, 210907, 3250853
regulator: 43215793482529633319.6918633012058181370849463190604824462771433171558456
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:30:27 UTC
last updated: 2026-10-19 03:30:27 UTC

(-42771283094872872640230/1369, 12497580309815663740913888605848060/50653)
(12915117446468112730, 203121098699814922971843832620)
(30490836814627080250, 215980081861046808185042068500)
(86066194458958429690, 768143280459136747704705281940)
(122521011865898593999, 1322338840216976424470557305090)
(-43056935874239587205, -159788405713400031487494251820)
(-13491545086015715575001108620821628817750/596149155156532544449, -3839706482888386266051256460584059741048387979233524764444500/14555676647812325402285008677793)
(3667380258472727605050, 222082860458865803019379673274900)
(-43244619587290483025, 157181711627378142569508393750)
(-52436185470065811280310/4489, 77631514524534737374591106426917020/300763)
(3910305909680947597465/144, 355282227848793099966008693612795/1728)
(-54291082638607605504279198230/1332031009, 9085462651038016782922965830498978173036140/48615135735473)
(-43836417035626120003572649823990/14533196691049, -13335451987827516599918040057135143879076643350180/55404077353074712907)
(55870380323882065346285975864200/26483858185009, 31050565490037250348118611892882926266337263578550/136292475733028011223)
(-1775097246807039992, 237668885246568811628760112326)
(161092281164786140165306/225, 64586590388061463518403556632680404/3375)
(191204264313903172171450/2209, 80449815995892417070754479886832300/103823)

X400, T=3228/8285

last edited by Andrii Prokhorenkov at 2026-10-19 03:30:27 UTC · history