curve #6147

← home · all curves · JSON ↓

y² + xy = x³ − 89001083140919071516077112371630505x + 10056745481571510867091006442891739161679494895544025

a-invariants: [1, 0, 0, -89001083140919071516077112371630505, 10056745481571510867091006442891739161679494895544025]
c-invariants: [4272051990764115432771701393838264241, -8689028096077785395574707552804635784848635680507433961]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 80916449453560600559900659805076064831722521425954725143589058836241018596302806604028030
discriminant (Δ): 1427991273178769979026880246247541855416142561929283536682519468150587886814635749722546226188495360000000 ★ record for rank ≥ 25
Faltings height: 18.9721
naive height: 253.0355
primes of bad reduction: 2, 3, 5, 7, 19, 79, 256706479659784272579869483217778829452499988661383601864119345313413339032082759443
regulator: 32365261447598665418655542.44483673632426787842151241330883378750043188059887520215173215
submitted by: Ritik Jain
submitted at: 2026-10-29 13:48:08 UTC
last updated: 2026-10-29 13:48:08 UTC

Witness: 25 independent points log in to add more points →

(198181292318374169199412374532354261787762/1306781171719924052557441, 10264596842809941619655233508342188136657268481384787882740763/1493840751612424056062044135819351489)
(1191604686625159829002/3721, -27234249895850872544931348311249/226981)
(296245643342543883914/25, -5097316425175323941365998433673/125)
(23883291636582627290, -116709860250483782372382229885)
(2102595435859614603312560/8473921, -1406152285956858626128239678157607605/24667584031)
(4238291587636041485/16, -4556198029551015162844005445/64)
(-330189608315172080, -58694101994442548681348555)
(2070948728124856010, -2950878560271327437884197805)
(5682129784154887617770/27889, -90903063323545268648065522247915/4657463)
(29715584421207426410, -161977469336147307088752600205)
(1115765880627499714202/1681, 34003154117039073174544057011307/68921)
(78569054232058586069/400, 99040894663200508865429111413/8000)
(893796776017840442, 802831044853716670107097667)
(451174039287852938705/3136, -2663831795289195410819850434075/175616)
(338239538095460029190/2209, 451742915368585964580701197285/103823)
(473008676971135799258/49, 10282497076477876857065238681413/343)
(3506287027486557079502419464740/24202788854689, -1698808004550449755815706609642662246510649085/119068838741560209137)
(9663351340487172122, 30025276456518698848133137667)
(3292656842951919410, -5951020015953799740714543205)
(704472405268491430010/841, -17642359319989473915755497399745/24389)
(46709380238916091390/441, 394896715834707625964130967295/9261)
(2378391387551467820906/25, 115990615373012863817169064829239/125)
(19770164377971919598/49, 68452922119043302822814135633/343)
(-7081972355142615766/25, -13995876475551243409808395337/125)
(401902053615407162, -198000912773211016409237629)

Commentary

No commentary yet.