curve #4183

y² + xy = x³ − x² − 12687403419773740800x + 14832398592309355212279298036

a-invariants: [1, -1, 0, -12687403419773740800, 14832398592309355212279298036]
c-invariants: [608995364149139558409, -12815192381014803764738185490277]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 396297680232994949376111983615607438010884782355764223510
discriminant (Δ): 35666791220969545443850078525404669420979630412018780115900 ★ record for rank ≥ 18
Faltings height: 9.9579 ★ record for rank ≥ 18
naive height: 143.5750 ★ record for rank ≥ 18
primes of bad reduction: 2, 3, 5, 153509761, 103202182382801471, 92647326004373073481586929123
regulator: 1725988596507163210.1089073614354578885731194256862510597563783161092110689
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 23:02:13 UTC
last updated: 2026-10-11 23:02:13 UTC

(-10242175, 122320666188644)
(57193958, -118772680600444)
(64505762, -118381856765590)
(-113713800, -127568203434094)
(-79010467, 125834625476336)
(-84513193, 126111294460415)
(-108760102, 127322461619426)
(91679657, 116918696800940)
(108320456, -116014554232918)
(189741398, 111498353378276)
(159272456, 113206302991562)
(-262379167, -134696735920444)
(195635915, 111165429523511)
(472898318, 94542359449076)
(-428875323, 142108722486595)
(527897906, -91004975234758)
(-492341992, 144774539650886)
(498129945, 92929970574859)

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