curve #3831

y² + xy = x³ − 8077025532831509874062079012713146690x + 8776419734991180261282971575187341263871691277445469636

a-invariants: [1, 0, 0, -8077025532831509874062079012713146690, 8776419734991180261282971575187341263871691277445469636]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 1529108655088467286102728130100835419136769737138957249682644526220220375684016884246 ★ record for rank ≥ 24
discriminant (Δ): 448597245691616428357458436372564565690179309287214251433013839483227168901248198752348505771019431620586995712
Faltings height: 20.0612
naive height: 266.5599
primes of bad reduction: 2, 3, 7, 11, 17, 23, 29, 43, 2203, 22477874349842222816746669, 137082944298583090081816824754998126221381367547
regulator: 463261904829387031949875.84677607860326544150753244381486210047502106408364506657462206
submitted by: 7fff-zip
submitted at: 2026-10-03 05:22:20 UTC
last updated: 2026-10-03 05:22:20 UTC

(-8649497536246218136084/3025, -484889661084375755619932825984854/166375)
(18241413163299815500/9, 23099342784429258371605583738/27)
(20469226540963688324/121, -3624353178772949118835523097110/1331)
(172718881529924395880/121, -524864334250134354619699160354/1331)
(2783766419548295918, 2804329301907414875306937314)
(1749259384405558580, -13434922063314182070814546)
(8009819622123779957744/7225, 668403830500641449042954538563702/614125)
(-2015360349515446876, -4107163652360523893856754450)
(209876239396392810068, 3040221985282868277919888961918)
(-419405981905496878, -3477096269589124113248320606)
(107543998334517572, 2812299403887271788382689614)
(142091630196956283551570/49729, -33316194873892776360450874375047778/11089567)
(879945447750404551261412/284089, -555842208515140381083585541052266154/151419437)
(1749096075570815876, -745966901222503407968242)
(82772370027608180978, -752619215498397145060024189972)
(-2254364957999691178, 3940550289030674693313932264)
(1450017564010429472356/961, 4660545124743006213600960443986/29791)
(19779979479416750605/16, -52798241310599230172459494469/64)
(372575872670494628, 2412225775211783352784531694)
(1496045697474314660, 202975856478017697565749614)
(24499608835493088740, 120483663093528398003102504174)
(2365361033810136085628/1849, -58279497984460215961895978760502/79507)
(92390913381417060050/49, -171645073355790483233408230258/343)
(1499149521005822660, -192388403166403808168714386)

X1008; T=-277/187; 2-neighbor step: yes (Q has vector q=[-1,0,-2,1,-1,1,0,0,1,0,2,-2,1,1,-1,0,1] in source section basis; h(Q)=12).

last edited by 7fff-zip at 2026-10-03 05:22:21 UTC · history