curve #2180

y² + xy = x³ − 21015960530302473341210266357147569830x + 17566852216331096945097199161461136733028723845196826852

a-invariants: [1, 0, 0, -21015960530302473341210266357147569830, 17566852216331096945097199161461136733028723845196826852]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 552172877067842717797110
discriminant (Δ): 460743701174262769908539198792865329234890207602408929929309488024368417354008778995122492348181216770418542240000
Faltings height: 20.5053
naive height: 269.4286
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 31, 41, 281, 419, 479, 569, 1153
regulator: 65742.560760939016343927974597783713475645486
submitted by: Tom Fisher
submitted at: 2026-09-26 17:02:38 UTC
last updated: 2026-09-26 17:02:38 UTC

(-323768234654667598073236376174/72977240449, -95528205831866792550988270101905028199626094/19714290666614207)
(14313485330700724862739929253151/16750995468804, 33087135823218327101262727287106584612554256751/68558440752730073592)
(-180780928705551339014149547355608/89374315532401, -6081165188483001212676838107943235738339842820990/844926814805897041399)

Found by Dujella (2006)

last edited by Tom Fisher at 2026-09-26 17:02:38 UTC · history