curve #2140

y² + xy = x³ − 1819834111904825898485099130x + 36464739063950913898627050323570640110052

a-invariants: [1, 0, 0, -1819834111904825898485099130, 36464739063950913898627050323570640110052]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/12ℤ
conductor (N): 48993786503812410
discriminant (Δ): -188697688268461759552991839632853465042097780092287671664811290518000169476161536000
Faltings height: 14.6944
naive height: 200.3175
primes of bad reduction: 2, 3, 5, 13, 17, 37, 41, 97, 109, 131, 3517
regulator: 20924.944026171572499925250392978065997389703
submitted by: Tom Fisher
submitted at: 2026-09-26 11:05:22 UTC
last updated: 2026-09-26 11:05:22 UTC

(66213461028264, -454160538272215775262)
(1587940304415908270265812/29276236609, -1562767430327834573698990964201257078/5009251912509727)
(869862688746765817528419089891604/39023947629422672401, -20359780037305447335448359004737922843369702455738/243779285717628367403603862649)

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