curve #1904

y² + xy + y = x³ + x² + 690560257169377937125059126423812540x − 33492188518937203020097127431557287129957999127407035

a-invariants: [1, 1, 1, 690560257169377937125059126423812540, -33492188518937203020097127431557287129957999127407035]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/8ℤ
conductor (N): 181623693748207975822425210 ☆ record for ℤ/8ℤ torsion, rank ≥ 6
discriminant (Δ): -21560417306163721410819519746735669379721765042269053423050290460335025621082324901752523978240000000000000000 ☆ record for ℤ/8ℤ torsion, rank ≥ 6
Faltings height: 19.6685 ☆ record for ℤ/8ℤ torsion, rank ≥ 6
naive height: 259.1820 ☆ record for ℤ/8ℤ torsion, rank ≥ 6
primes of bad reduction: 2, 3, 5, 7, 17, 19, 23, 31, 37, 43, 47, 61, 101, 263, 463, 66943
regulator: 1342973.8146145281505529048264135548307826869161093
submitted by: dujella
submitted at: 2026-09-25 17:53:03 UTC
last updated: 2026-09-25 17:53:03 UTC

(286126088836986533, 433035480275757031966872273)
(121390141610245853, 228306310388654208874997073)
(377567526557995573, 530156507956449179371813753)
(210538669890805853, 348180841544471134046597073)
(20853081120020405853, 95301363213306571952478597073)
(326728698269569003, 476458277653995656563456173)

found by Elkies (2006)

last edited by dujella at 2026-09-25 17:53:03 UTC · history