curve #4610

y² + xy = x³ − 7117309472751389992340x + 225721145785821631884013832802192

a-invariants: [1, 0, 0, -7117309472751389992340, 225721145785821631884013832802192]
c-invariants: [341630854692066719632321, -195023069959462336229826051620542369]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 226188988947065319188364799890
discriminant (Δ): 1063830908058815520250470895893151711029167651581066037090002560000
Faltings height: 11.4502
naive height: 162.5641
primes of bad reduction: 2, 3, 5, 13, 19, 31, 41, 103, 127, 131, 151, 181, 419, 829, 1069, 1381
regulator: 16539072.68830650558279202315423831988569464737334414780319
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:22:17 UTC
last updated: 2026-10-19 03:22:17 UTC

(-44324403596, 21309869223446428)
(11832101992, 11965147336367308)
(20794607524, 9311885407800988)
(71708332252, 9169538120773960)
(814125828544, 730776329574212908)
(1380142516164, 1618421111308168608)
(1767397095024, 2347008201133493988)
(5071913235472/9, 11300966664827184812/27)
(190441396446946/4489, 108818959840688387464/300763)
(299983618505416984/4950625, 45333500205847441134622652/11015140625)

X720, T=-34.

last edited by Andrii Prokhorenkov at 2026-10-19 03:22:17 UTC · history