curve #2178

y² + xy = x³ − 1501011456398147086648544266758850x + 22251270940723503314374317274872523646621572635332

a-invariants: [1, 0, 0, -1501011456398147086648544266758850, 22251270940723503314374317274872523646621572635332]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 1232601651505117906530
discriminant (Δ): 2545810604635477990891629919901547654018238550440512005821410533307298089135766417299626798267040000
Faltings height: 17.9084
naive height: 240.7879
primes of bad reduction: 2, 3, 5, 7, 19, 29, 41, 43, 47, 73, 173, 809, 12583
regulator: 20379.425375600879704846808082746061928648501
submitted by: Tom Fisher
submitted at: 2026-09-26 16:48:03 UTC
last updated: 2026-09-26 16:48:03 UTC

(585150090442017404, 446653884639086830911813998)
(60858503151041321123234/271441, 14802686107078222471948784650679698/141420761)
(288266315903991120130014776246/367947788569, 154585670444642553138450754364572706622327814/223192345224704003)

Found by Rathbun (2003)

last edited by Tom Fisher at 2026-09-26 16:48:03 UTC · history