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curve #2027

y² = x³ − x² + 3090014805x + 27966726311676

a-invariants: [0, -1, 0, 3090014805, 27966726311676]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 334879589896641804408
discriminant (Δ): -2226167806508554533311120405808
Faltings height: 4.5118
naive height: 77.1679 ☆ record for ℤ/2ℤ torsion, rank ≥ 9
primes of bad reduction: 2, 3, 17, 31, 37, 41, 59, 89, 373, 733, 12157
regulator: 79867449.433627728113542727750419482295989490063924135394
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:03:12 UTC
last updated: 2026-09-26 05:03:12 UTC

Witness: 9 independent points log in to add more points →

(-6019, 3024869)
(-907, 5016307)
(-8539, 978979)
(4861, 6565221)
(-8387, 1208613)
(25768, -11166882)
(34021, 13132701)
(1170472/9, 1384516666/27)
(43613, 15674363)

Commentary

2-isogenous partner of curve#1371 (Michael Rubinstein).

last edited by Steps Unbounded at 2026-09-26 21:42:44 UTC · history

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