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curve #2034

y² = x³ + x² − 2056755905x + 27106485989599

a-invariants: [0, 1, 0, -2056755905, 27106485989599]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 6682940617328192 ☆ record for ℤ/2ℤ torsion, rank ≥ 8
discriminant (Δ): 239404129080612165698398748672
Faltings height: 4.3475
naive height: 75.9468
primes of bad reduction: 2, 7, 31, 113, 193, 233, 281, 337
regulator: 4342493.22634285510493787163028908016061520492349797406
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:05:05 UTC
last updated: 2026-09-26 05:05:05 UTC

Witness: 8 independent points log in to add more points →

(-8451, 6624548)
(7194, 3561257)
(37917, 1906604)
(14649, -347648)
(47709, 6129908)
(-267887/9, -212522968/27)
(59337, -10676456)
(171897, 68941264)

Commentary

2-isogenous partner of curve#1351 (Michael Rubinstein).

last edited by Steps Unbounded at 2026-09-26 21:46:30 UTC · history

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