curve #3721

y² = x³ + x² − 5100446049204850223511073745x + 137488064201527560952142742891541383860019

a-invariants: [0, 1, 0, -5100446049204850223511073745, 137488064201527560952142742891541383860019]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 10142674384910056605378619013722350501344515415761291339100408498665246414632
discriminant (Δ): 325809640186477339275105128332862344666117406187196939801701771662100169732457102592 ★ record for rank ≥ 22
Faltings height: 14.8122 ★ record for rank ≥ 22
naive height: 203.0110 ★ record for rank ≥ 22
primes of bad reduction: 2, 3, 17, 213696269, 3598663233216516383434289, 32326164135403689927690302137136189908819
regulator: 10591661684131573744248910.12437983098272214810646510726205458306342035395001834055
submitted by: Matej Jurasić
submitted at: 2026-09-30 19:58:29 UTC
last updated: 2026-09-30 19:58:29 UTC

(-72312219314285, 358033401272404081962)
(-58391101283909, 486027835618841045226)
(27995494535113, -128995967208295122750)
(-66585650012969, 426482348156469577026)
(51058925248369, -100876636560466163322)
(5827395151870189/4, 444323125766713996364067/8)
(842425512791779/25, -7787040149920062984642/125)
(71649835242430, -373992813814656767337)
(99685134354847, -787167806797740387906)
(67413196979695, 316247689879502171262)
(13323841336615, -268133999841763710462)
(46201618854913, 21463789399682586570)
(3160861720827871, -177663539090100261123774)
(-10519178077337, 435863034364206063870)
(52299949624249, -117431879787607514958)
(5732079687565366/121, 62122983096952142435319/1331)
(27563732289913, 133575962405680563570)
(13567919973123145/289, -190965221736131563159806/4913)
(-105923824850355125534771/4553280484, -151628823766619184839700335083914723/307246260499352)
(131367544975071434361571/3785571729, 11124663516896492187027953477658586/232914871770183)
(19254427731479158290811/244828609, 1808133593143301559781019440511274/3830833245023)
(1420257743526623355731552161/39118207347025, -3154148956864624929630234142242709365834/244663067532637246375)

Specialization at T = 12/19 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-09-30 19:58:30 UTC · history