curve #3541

y² = x³ + x² − 46996888851152389615709446801641x + 124173094457485325498787900246354986964406024359

a-invariants: [0, 1, 0, -46996888851152389615709446801641, 124173094457485325498787900246354986964406024359]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 6260499432444497268910560769460650180044272659610986692140281226345069566080
discriminant (Δ): -17637029242593424015271837078957075210933850670402541798553794738266239107287761953143743897600
Faltings height: 16.9837
naive height: 230.3992
primes of bad reduction: 2, 3, 5, 7, 11, 19, 41, 584897, 80536377720427, 14053156694287706720783, 82117211608392339063231389
regulator: 1602852903871306570967304518.52042186562104500317380965899208571483959798120589837788
submitted by: Matej Jurasić
submitted at: 2026-09-28 00:31:27 UTC
last updated: 2026-09-28 00:31:27 UTC

(4060845490140675, 17065321180981760191428)
(4409212200850509, 51710775989770393978020)
(4792037967356274, 94893600454088421083175)
(-4062638880610641, -498046671285414657138180)
(11316949478935119, -1020642571316136735032220)
(3195204399610209, -81420686909079984366120)
(370106631178200471/25, -204366944532575801601027444/125)
(3518772613173837, -48686030122057620246108)
(-7910680169582479, 30151258522120201952640)
(4164386521430259, 26060590008308981188980)
(1150836316598293811/289, 64328653795534688471165100/4913)
(4940951428453059, -112192698558727023971580)
(4144358736356319, -24154266782689671709620)
(3989387682728355, 13275691291501324934052)
(4562813401129695, 68771263706543805545292)
(-640879121951737670/81, -19437445589660143894746667/729)
(6466263552243192983823/1495729, -77535592809749478354632575195764/1829276567)
(481095988802762117265/53824, -8075380988504560720430789439399/12487168)
(9582787000189576842440414859/1666936627801, -451366530311775436964688155235558969254220/2152180213217243299)
(10646910366100087071336039999/2418849220225, -191417431684691743855627192040080874485332/3761951532493234625)
(633728867642307057015/243049, -16672042691998683006073206612924/119823157)
(46866602881496092527397774611/19584811273729, -13816706355095239917074889769723502941683540/86672053501983298817)
(2709041979244681726165989/9665881, -4457536102818916682365571260546724580/30051224029)

Specialization at T = -8/87 of the rank-17 fibration of X1008 (equations as in curve#751).

last edited by Matej Jurasić at 2026-09-28 00:31:27 UTC · history