curve #3726

y² = x³ + x² − 64816289480794184827003020x + 201241650158899013718159834147497740368

a-invariants: [0, 1, 0, -64816289480794184827003020, 201241650158899013718159834147497740368]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 121699625558132826973404258275555968548692611342661702520 ★ record for rank ≥ 19
discriminant (Δ): -67828335296597323570807286969368581981242864972418994412275529759466156000000
Faltings height: 13.6247
naive height: 189.9183
primes of bad reduction: 2, 3, 5, 7, 11, 19, 47, 4457, 259564121, 1813248433, 370056132262939294021750819
regulator: 180440913574672990.4777079277004407953449040264740242936968758093909782516764
submitted by: Matej Jurasić
submitted at: 2026-09-30 20:07:57 UTC
last updated: 2026-09-30 20:07:57 UTC

(3297380790606, -4834165970905806150)
(7474578969606, -11591673768650433150)
(5603463829866, 3740052832634873370)
(-277859708994, -14806418643630271350)
(17702371196349/4, 8276186906466199875/8)
(-11564648277651/4, -152728643006649373125/8)
(1776479118162, -9576179658283676130)
(5098676951886, 1819922584001562810)
(4497953550531, 837690563467226700)
(-51841185588759/16, -1243045217888653649085/64)
(4400502463248, -1109321882166668148)
(-1498855646694, -17176281033399122250)
(4654546902446, 625340245991521830)
(4551115024743, -721737227924563158)
(4569365838156, -690345234384365700)
(5305016060862, -2586560861580675210)
(-117397661794014/25, -2506432117195506696966/125)
(167712250421178246/32761, 11234982559078522413613290/5929741)
(235002617190808908/175561, -795259649893447540037559708/73560059)

Specialization at T = -3/2 of a rank-17 fibration of X1092 (two 2-neighbour steps from the one in curve#1879).

last edited by Matej Jurasić at 2026-09-30 20:07:58 UTC · history