curve #2183

y² + xy = x³ − 1621197495376612287530904105233724120x + 792688598791865073857094426358748343551798168746190400

a-invariants: [1, 0, 0, -1621197495376612287530904105233724120, 792688598791865073857094426358748343551798168746190400]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 22123123074505561909710
discriminant (Δ): 1252185127314321713760646224934127454630602571758499450589216822946034192444960728113935462494640537600000000
Faltings height: 19.6166
naive height: 261.7423
primes of bad reduction: 2, 3, 5, 7, 13, 17, 31, 67, 73, 151, 337, 1049, 58897
regulator: 267843.50255865834455896981325658218195862644
submitted by: Tom Fisher
submitted at: 2026-09-26 17:19:51 UTC
last updated: 2026-09-26 17:19:51 UTC

(184265049963459555715756173360/183152329369, 33252887250675563312176497099144406413258360/78382420333745347)
(82783276094283429032303138646750640/107935148321592201, 747042050857350584081590197310444933406960306538680/35460457871497193838297051)
(883193138665626092244648865044768278534403013785057249004972327632/1015272818993790179595312025606995606967976322481, -206355224855206696230997552878641266346125995941713540380329699739899409129414382783494501582099048/1022996479223612825011249658698109282807737802426954717854552678271406871)

Found by Flores - Jones - Rollick - Weigandt - Rathbun (2007)

last edited by Tom Fisher at 2026-09-26 17:19:51 UTC · history