curve #6211

y² + y = x³ − 1052028458706885127x + 415051418389439686950056766

a-invariants: [0, 0, 1, -1052028458706885127, 415051418389439686950056766]
c-invariants: [50497366017930486096, -358604425488475889524849046040]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 14082352251121012773554757156671550787147781614127491
discriminant (Δ): 98576465757847089414883300096700855510034471298892437
Faltings height: 9.1007
naive height: 136.1054
primes of bad reduction: 7, 4861, 413858178832133681298814387300424685900837029833
regulator: 3579332558577033.70641007380753522590581758814641024717187350480288364361
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-30 17:20:21 UTC
last updated: 2026-10-30 17:20:21 UTC

(-35161049087/49, 9704370668708897/343)
(-44374540022753/54289, 341499816560447007027/12649337)
(-4736293207/4, 6321672920407/8)
(1233396105, -31524706417768)
(15508786031101/18769, 26960301793921365423/2571353)
(15679008884/25, -174191380779402/125)
(163698853459/121, 50995747755141073/1331)
(1928520937/4, -35694394682751/8)
(2377188934/9, 336801930167105/27)
(2754034470445/2809, 2688237654636339384/148877)
(3213238367362954/2785561, 126164574297421521710192/4649101309)
(38335346998, 7503177077111628)
(411807397/9, -517252780859608/27)
(5347501497/4, 299111426766393/8)
(567780077, -876513656505)
(6400524733/9, 139157108090333/27)
(6493679619, -517115254159029)

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