curve #6208

y² + xy = x³ − x² − 1130091988529486542x + 459519459333275218859197216

a-invariants: [1, -1, 0, -1130091988529486542, 459519459333275218859197216]
c-invariants: [54244415449415354025, -397024812619849919571977301525]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 869068663038422178215828463165696564060441707350
discriminant (Δ): 1147648622975388407442912277033460597670016296641042500
Faltings height: 9.2050
naive height: 136.3201
primes of bad reduction: 2, 5, 7, 11, 2039, 12757, 8678158532651857651311904145260270757
regulator: 1816910067720194.29705817674455713092438856041847859958514359164625825693
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-30 17:19:55 UTC
last updated: 2026-10-30 17:19:55 UTC

(-1000575786606/841, -267113456007975478/24389)
(-100167046, 23910558563458)
(-1004019507946/6241, -12445257081049745498/493039)
(-100640176, 23921437977528)
(-100652853539/11664, -27288705833530771049/1259712)
(-1006879600306/841, -239449765653453048/24389)
(-10096880294809/11449, -33998568180595671961/1225043)
(-1011377346, 23832145412488)
(-10121294248421/14161, 50614825885571234272/1685159)
(-1014643070, -23697253225156)
(-10200986672198/8649, -9906439095947880374/804357)
(-102163152203714/522729, 9803895991415251311656/377933067)
(-102451886859/289, -140307268219427806/4913)
(-1025267759/9, 654036971484946/27)
(-1027053344485/1444, 1649368549820378807/54872)
(-1031177698047/841, -32635286152002338/24389)
(-1036924336, 22725521711928)

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