curve #324

y² + xy + y = x³ − 10006641313567584974778494x + 12262133853164892979587951115335032676

a-invariants: [1, 0, 1, -10006641313567584974778494, 12262133853164892979587951115335032676]
c-invariants: [480318783051244078789367689, -10594483649135188012538566629767652283813]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 32831599583121109539308074244197311418694161772495232034577990
discriminant (Δ): -827890380662473353353262961988651839315200656707032287836414008796126120900
Faltings height: 13.2062
naive height: 184.3223
primes of bad reduction: 2, 5, 7, 11, 13, 23, 29, 378258572048653797353702395450211320437078338251475569
regulator: 74125103574956268.845573141840988578032122833610296298396600893810891225339
submitted by: Andrii Prokhorenkov
submitted at: 2026-08-24 13:27:47 UTC
last updated: 2026-08-24 13:28:53 UTC

(1763783477288, -315589181210643757)
(2460412536414, -1592513362028315143)
(1529436046971, -731597583865915183)
(1756181653058, 324072818182422893)
(1669005285208, 458411741228296868)
(1364023898538, 1072699599101871968)
(3644164094403, -4918389977752071237)
(46900821226784, 320484095765121058123)
(1535538842670, 719139724381607112)
(2970708571663, 2958401280087662993)
(1866577950839, 295510114825552903)
(-1478612883916, -4881125882801259508)
(4609878060277/9, 72805067699599223741/27)
(51860447219539/36, 197543090465009187917/216)
(121032646889469/16, -1230110677613430588637/64)
(1835384178733, 280787686507360343)
(-977251254147, 4594327655958540083)
(46026199699284/25, -35262804348147411108/125)

No commentary yet.