curve #2181

y² + xy = x³ − 59654254810332161499933732539083310x + 936036113034275895945648528397370958419427728893572

a-invariants: [1, 0, 0, -59654254810332161499933732539083310, 936036113034275895945648528397370958419427728893572]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 845032799355123544410
discriminant (Δ): 13207892700205220869377302474994855855931950230834017533541093417086826090443820534000909791438636900000000
Faltings height: 19.0528
naive height: 251.8352
primes of bad reduction: 2, 3, 5, 7, 19, 23, 37, 47, 281, 1447, 1933, 6737
regulator: 82701.635872755999631710703056800489382282465
submitted by: Tom Fisher
submitted at: 2026-09-26 17:08:23 UTC
last updated: 2026-09-26 17:08:23 UTC

(423636398364728130558/32041, 70153524044528407532259723512964/5735339)
(-212218555436959806104/1369, -4070672727584190624828727982726/50653)
(8452319722523363921569428256760017402630395565491507482512250164/59692072868085173675728631193552258578545561, 777075522029540793165779905112440827567904945232388550670644286763642232436234047429573571171782/461184805928472795689461276558991227050395203450511219660991605059)

Found by Rathbun (2006)

last edited by Tom Fisher at 2026-09-26 17:08:23 UTC · history