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curve #1818

y² + xy + y = x³ − x² − 15017634212x + 4999380048647111

a-invariants: [1, -1, 1, -15017634212, 4999380048647111]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 29733210
discriminant (Δ): -10580543065286139623768064000000000
Faltings height: 5.2092
naive height: 85.8193
primes of bad reduction: 2, 3, 5, 13, 43, 197
regulator: 3.547484620886939973983871142787103121412
submitted by: hdeping
submitted at: 2026-09-25 15:21:48 UTC
last updated: 2026-09-25 15:21:48 UTC

Witness: 1 independent point log in to add more points →

(-23259, 73060189)

Commentary

Specialization t=-5/8 of the Kubert X_1(9) universal family.

last edited by hdeping at 2026-09-27 08:53:03 UTC · history

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