curve #624

y² + xy = x³ − 28855782933375676695985173952745496x + 1760128919948594878841603687863332325309254524621376

a-invariants: [1, 0, 0, -28855782933375676695985173952745496, 1760128919948594878841603687863332325309254524621376]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 113492893163216590951326900190230978222582452610473766586860712405885559618730
discriminant (Δ): 199365348233842335315740094591552663732728483291546237511787380316908018948610623111382603759419024998400
Faltings height: 18.7586
naive height: 249.6565
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 43, 199, 479, 509, 1423, 10243, 386927119, 16905330428514262074505824304717005225161229677
regulator: 9967965195709552790421.19683262164504850183564234362656518773770072937175689874856139
submitted by: wgxli
submitted at: 2026-09-07 07:16:15 UTC
last updated: 2026-09-07 07:16:15 UTC

Witness: 23 independent points log in to add more points →

(-20449977135958434775990327806096/478035064464169, 564421304129419199160741997468448181422454612744/10451764863900429050197)
(4246931086985150431897523174832/59742495872929, 3810155146851290136573517600127814483082240920/461769286398018688783)
(2589810779643989700567337764552/172218824429089, 82410256525069374809057656116242653337977921680/2260065004467836059313)
(1470742118595870244272/5929, 45346577688679904678615473430280/456533)
(239995655357404412131425/1982464, -17880635246012339691843586087189713/2791309312)
(4636578375033927094873175564640/61395389341441, -1642077183677564759949759230350734770648773704/481064862488037125761)
(31427594930219358096/625, 326365678003390271505857647656/15625)
(667184141743388310676779216/588984361, -17048982919915081345101237078454036770552/14294061457109)
(210963489104561563248/961, 2308511805627750958523735881752/29791)
(-55380556696587901228954889691714774/2410729534226551561, 183785800138312535245291986268864308947768798878820118/3743025042871598575214876059)
(836619687377546895792/6889, -3915123022919854861996020364296/571787)
(81360304470439862795136859824/1133736241, -23206926783463834106344559115733528978741032/38174032970711)
(53121951713890126192920484896/197883515281, 10174556531567647946465241183199232503311672/88026700821115321)
(273438979339578979307036682384/1991606805049, -55248366627566026703326410897817198572776136/2810641162377765907)
(-193638608997558486, -9330946264282638687392892)
(4323659361622189155358794859074/12617009473849, 8031251230943929679654035586399320425137833164/44816160182519023507)
(935727694293388032305910335260572197202864/6728796629534393384580289, 364724468884660552574536322938289092992389168087120419689065064/17454447393742404517771387744793986337)
(7867041746770892921504165422926977376/26339045931986004361, 19014972055276763957458910326173568338913385938014571368/135176145792651300877075120859)
(1424856924947222994296430000144/8784792127225, 955542492861378868635377145925477650044692248/26037377157764085875)
(671339544289570524046721244444586896/3166313688718927321, 405251819634025418288355038724996593090969684722177512/5634182465980498608038996381)
(73680515416401865234055450001279455165808/389112609080837634482161, 13482763343907199422180393734976909655816408194485207761437672/242724131795937845743336484059776841)
(14094978897679385336363776/37564641, 48162242556524094668564838570048970648/230233684689)
(505988124833506227775480864837884/3282915841660225, 5870445396457598929892560149352937863782033013128/188100359006907871865375)

Commentary

Specialization at T = 127/479 of the rank-15 fibration of X948 given by: y^2 - (Lx+B)y = x(x+D)(x+E), where B = pq(L+p+q) - pE - qD, L = 98592989T^2 - 42403052T + 4534724, p = (202T - 95)(1195231T - 296423), q = 1385553T - 317733, D = 117(202T - 95)(8476038568T^3 - 1313273454T^2 - 1327786629T + 273595195), E = 117(3843642919175T^3 - 3332578517195T^2 + 936871679129T - 85951271349).

last edited by wgxli at 2026-09-17 17:35:12 UTC · history