curve #4624

y² + xy + y = x³ + x² − 5381092633596686364075620574185495465x + 4803175029872159734905357462656941157976629636085277847

a-invariants: [1, 1, 1, -5381092633596686364075620574185495465, 4803175029872159734905357462656941157976629636085277847]
c-invariants: [258292446412640945475629787560903782321, -4149943225809546012895422195830404251559031412284458427369]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 236536244628704799119256780694743964878896550193854791627591910
discriminant (Δ): 5757322267308353824093020536862878047415962451225006315924286045607788141127955441967215621663611905600000000
Faltings height: 19.8418
naive height: 265.3415
primes of bad reduction: 2, 3, 5, 11, 23, 43, 53, 71, 107, 113, 139, 149, 191, 263, 277, 311, 337, 401, 1723, 2777, 9173, 31601, 47969, 137453, 143813
regulator: 191552467238551277.026965140582041198948851870753059049118164243346887275
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:31:06 UTC
last updated: 2026-10-19 03:31:06 UTC

(-2667070462305680193, 428193501362196809175447496)
(-2362405682777344593, 2081106866906172294260162296)
(-730075234020336593, 2888362893875111485913886296)
(-2749666849606032537/4, 22876915809167236243213326563/8)
(389349922150443855, 1663451200034205546651820888)
(976789973694741807, 692063025207320101828773496)
(1049760911193267907, 557807060595071790257637296)
(1423044861253822407, 165485067662368119683669296)
(2416805205404020691, 2431985694708260077261969244)
(2530074145004238367, 2717409153009600241993470776)
(3058227353946703407, 4116967345734789784402706296)
(37560266110635195957, 229764486743937928231728552346)
(11803946270239849063/9, 1107786078036411770892041192/27)
(64102767722397306443/49, 17017635503497616982497308028/343)
(381191450289992501873/289, 78968437511943875865925616248/4913)
(395284040219396634063/289, 213799213517458021123316898488/4913)
(16819608342569038671947/11881, 194254917488394806882545659727504/1295029)

X400, T=-577/3960

last edited by Andrii Prokhorenkov at 2026-10-19 03:31:06 UTC · history