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curve #4312

y² + xy = x³ + x² − 2179271791x − 9516362821775

a-invariants: [1, 1, 0, -2179271791, -9516362821775]
c-invariants: [104605045993, 8221352940168715]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 293853198970733402778
discriminant (Δ): 623275652125933552840414259844
Faltings height: 4.4079 ☆ record for ℤ/2ℤ torsion, rank ≥ 9
naive height: 76.1204 ☆ record for ℤ/2ℤ torsion, rank ≥ 9
primes of bad reduction: 2, 3, 61, 73, 79, 97, 109, 673, 1993, 9817
regulator: 617635815.08967756191783748354757447058195491486180902564
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:49:45 UTC
last updated: 2026-10-17 09:49:45 UTC

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

(-12214, 3914987)
(-24273/4, 14957927/8)
(71844, 14273153)
(131844, 44599553)
(-261165200/13689, 8042049153035/1601613)
(-372104/9, 85565621/27)
(108127051/2116, 342438086647/97336)
(730158841/14400, 5515923501679/1728000)
(1071853037/16129, 24094949245337/2048383)

Commentary

Curve 2-9.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 09:49:46 UTC · history

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