curve #4018

y² + xy = x³ − 66127330028977556504838734952580765179493x − 2958400401188568925756817079226988035840232240587215637255423

a-invariants: [1, 0, 0, -66127330028977556504838734952580765179493, -2958400401188568925756817079226988035840232240587215637255423]
c-invariants: [3174111841390922712232259277723876728615665, 2556057946626923551849128788690031278897612266950768495495761975]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 608480130869274673011093246882337748935299188663528462593209259950
discriminant (Δ): 14725520879464003410482889962294353725325097436344970243714146812376316203416042032360017287336937170105961887375155951168000
Faltings height: 22.5204
naive height: 293.5908
primes of bad reduction: 2, 3, 5, 7, 17, 19, 23, 43, 53, 61, 101, 167, 233, 563, 587, 607, 1033, 1123, 2473, 9161, 67271, 97987, 3788861, 25217561
regulator: 6158642925084880311390825449.71079424890126790075614267437847057266189715
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:46:55 UTC
last updated: 2026-10-05 04:46:55 UTC

Witness: 17 independent points log in to add more points →

(453358467784461190337371/100, 304758563245016225449785664623952051/1000)
(-32330935312804639752618171967215284226778972/643905877533831458960401, -250641705343154538410510335957971519641092565741500640432933929603/516694196976743861380578542272500601)
(226441399109839715825054012782154813025734/721820765157179841169, -51927969847183479035880891041162631424976475192754034330425187/19392958021144098333029976245447)
(7485500981660996240506413293565254/146516700625, -647628274656251146665195597352188510739080071964167/56082930081734375)
(13662953414919025777190242016044175158/31427198903306761, 39577370992629772380333791520891225182008748398657694375/5571325228304514168320741)
(78984828798024095218648634750001956/185158368358681, 17172946955159598866193824706070765029933933250097935/2519503799341764743171)
(-8854132747489221584325389978570646958726/161756020117106020225, -1450693690681239243947250037179873431402565371753041596951887/2057267092786413780388895453375)
(-18917198913417933378710204320812468759466/375401722423265222689, 3606944809550585218563985354221382301925628313058680627440133/7273515880622236431563644343887)
(-149607588523535355120790357432822526494/1326046050545851441, -2673829362603306812704148707686299381316613256707205897489/1526996035733140616294840489)
(767692147821992965785584544028089204314/561044003910091849, -20879138078190990412146138667935418438315094414141802014003/420238064818879041907709243)
(12169190460043764819411880467049057127894/42439719417194277025, -355793578664061426528360082580614704379558437518130914257807/276476839311779576462089471375)
(3684530494227606831190212368907733298/13189369660890361, -920659242787224698379464197436700577382547120360665605/1514732908106929952128141)
(103509248362404538588493793533268933682853462114/179496769218928554850171009, 29519029664409727397653123718368381431955542613539592647386771166139495/2404833173195044871839691123795156675777)
(-29430531133062154366553091448605650478754/197867329230826353121, -5271202089918235056766524029421250624806280258849049049064259/2783307165670245968787344767919)
(-27527365192671193289763661044307755593870228056/121032607924370789836060369, -749196457091435005572828494196390318981769591619179649737449553089545/1331538066998560534263509821821531200153)
(165903886265539388195751605380708973675549271998/4117264762972862834624641, -67573433297833681300250257041285160572592422902182256709847442927780275/8354360144796420215258540126845205311)
(380131134362263177780198460747520806910788486/239281401101192338839721, 7310886358008775960926538409001763650092998039988101635578729256085/117047842935974244606605832088314731)

Commentary

Unlisted rational-isogeny neighbor of curve#3692 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 17: 17 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:46:55 UTC · history