curve #6206

y² + xy = x³ − x² − 1684682326126354x + 32652901284755510741824

a-invariants: [1, -1, 0, -1684682326126354, 32652901284755510741824]
c-invariants: [80864751654065001, -28212106346137378837643445]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 77297336565051466013441574930658468289643609454
discriminant (Δ): -154594673130102932026883149861316936579287218908
Faltings height: 7.7694
naive height: 117.2036
primes of bad reduction: 2, 23, 1027461148495633, 1635465131026399086819464975953
regulator: 142462520472249.2375068281926471866708407252997114504907197072733470139
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-30 17:19:36 UTC
last updated: 2026-10-30 17:19:36 UTC

(-29812120, 237461653812)
(17659478176102/57121, 73593066135543696570/13651919)
(222181994/25, 16947254457912/125)
(230271077, -3443193683987)
(2562552842979208/82973881, 75874030606198526029548/755809082029)
(295895309640/7921, -104216593707250532/704969)
(3330811883/121, 112426054532172/1331)
(39095106, -162943130386)
(42759155/4, -1007710707951/8)
(4656427753/256, -367029242058675/4096)
(4776831638, 330134409147750)
(503349650, 11256469595968)
(5370949433/256, 331270827526827/4096)
(638996775173/2401, 505117277581418685/117649)
(857865505, -25098619085067)
(87938421, 751319451085)

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