curve #4186

y² = x³ − x² − 357845172766698640x + 82774132683222642097318096

a-invariants: [0, -1, 0, -357845172766698640, 82774132683222642097318096]
c-invariants: [17176568292801534736, -71516850535244953015273626560]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 141600662499554807601482648291199596800089565737744
discriminant (Δ): -27187327199914523059484668471910322585617196621646848 ★ record for rank ≥ 17
Faltings height: 8.9057 ★ record for rank ≥ 17
naive height: 132.8795 ★ record for rank ≥ 17
primes of bad reduction: 2, 3, 467, 863, 10859573, 674036822407191264883315817786000491
regulator: 1705725072350440.53724283474765759396754556821466395196501557015100616718
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 23:04:50 UTC
last updated: 2026-10-11 23:04:50 UTC

(372966808, -1091340928668)
(-117575116, -11100561823272)
(349398196, 630786681576)
(282723084, 2049819521272)
(839351320, -19332569620836)
(378443566, 1245166630614)
(298348753, 1602524350788)
(73332334268691124/222875041, 2689568402771565013511592/3327301487089)
(12842330621656/11881, 40101696825132661836/1295029)
(1212876598, 37854696382842)
(2777645752/9, -35516476633076/27)
(291177631948/961, 43840699694935848/29791)
(-222079487, -12300056931048)
(61757306121/841, -183959044683733216/24389)
(543802648, 6999358308708)
(149511439161580/243049, 1170493796048441836248/119823157)
(442417938124/289, 274538215354075032/4913)

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