curve #4649

y² + xy = x³ − x² − 135106943487621085899x + 437436449661005173548681415393

a-invariants: [1, -1, 0, -135106943487621085899, 437436449661005173548681415393]
c-invariants: [6485133287405812123161, -377945092477925370152734588345341]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 3368735979785622317933377456962690
discriminant (Δ): 75175033471068593099472916673065691599561201303936225538284500
Faltings height: 10.5804
naive height: 150.6714
primes of bad reduction: 2, 3, 5, 11, 23, 53, 73, 131, 193, 277, 293, 479, 1993, 3373, 7207
regulator: 15978000433.091697623648259461898368914850181803609335342663172
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-20 15:07:47 UTC
last updated: 2026-10-20 15:07:47 UTC

(-9137898096, 953421918684305)
(-3495046057, 931102300418426)
(-8619090431013/676, 5194137873212354509/17576)
(25834483172, 3766880046932369)
(14142912983/4, 501916550846347/8)
(38422021459314/3721, 85920717371297673871/226981)
(275229147152, 144264058079121809)
(2992725794, 244748349827315)
(78702187952, 21846889105889489)
(114480161252, 38539712597202059)
(235430201389001/69169, 2372253123950386888702/18191447)
(35764861139597681/1261129, 6240169370215835602186247/1416247867)

X720.

last edited by Andrii Prokhorenkov at 2026-10-20 15:07:47 UTC · history