curve #4143

y² + xy = x³ − x² − 512438769951095288821x + 4378142507111394763592020181713

a-invariants: [1, -1, 0, -512438769951095288821, 4378142507111394763592020181713]
c-invariants: [24597060957652573863417, -3782715126033558301434068854614669]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 93005183735730287397214853501626466469072789089680046
discriminant (Δ): 331404594984264274677517070327178263394757918481759165442136084
Faltings height: 10.7840
naive height: 154.6707
primes of bad reduction: 2, 13, 19, 29, 53, 450043417, 1611540521, 168892628674756444991716093601
regulator: 1422290798492407360.91341186341942069358879639825288496202574752416977213
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:07:24 UTC
last updated: 2026-10-11 01:07:24 UTC

(5053479890350684/273529, -157809702326621656531129/143055667)
(259066732301/25, 53135874791898236/125)
(-16394582061, -2893568854503236)
(566006710448/49, 4110357933321375/343)
(-755817237797/36, -523879897445463901/216)
(1559995443158/169, -1448152292969532539/2197)
(-22780476589, 2056661821075953)
(368730293919/100, -1593350155748234117/1000)
(102942224476/9, 3110562458308253/27)
(729928494061/49, -76865781557246604/343)
(10741674091, -336316045746724)
(411778240477288048/23551609, -99863509918678218322957659/114295958477)
(-24184845269, 1620356453200121)
(328895528, 2051740380717703)
(14718174094, 155873269414317)
(566816076852016/37249, 2317860476595751324089/7189057)
(7369211452976861801/236421376, 15715173380433352043708911843/3635215077376)

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