curve #4077

y² + xy = x³ − 13154430044998166408334766342289072369695507714592225863x + 3083796367935175198261803587644229589618481982519584801998918474644084142165694217

a-invariants: [1, 0, 0, -13154430044998166408334766342289072369695507714592225863, 3083796367935175198261803587644229589618481982519584801998918474644084142165694217]
c-invariants: [631412642159911987600068784429875473745384370300426841425, -2664400061895991371298198300671733328670236414297024445571878772710565254281800065625]
rank (lower bound): ≥ 21
torsion subgroup: ℤ/2ℤ
conductor (N): 36002324741262229107384053035934129095312333739830493609470477957959545215672356665910453744176850
discriminant (Δ): 141570474394307308670994893489221815049678392028500055004898664789887063759828864677118003568322830025639551910651409799768906597079579842375660878784670892001704000000
Faltings height: 30.7634
naive height: 392.3627
primes of bad reduction: 2, 3, 5, 7, 13, 17, 37, 43, 53, 59, 73, 211, 241, 283, 331, 337, 347, 397, 457, 619, 967, 2861, 4603, 5413, 5641, 6607, 7487, 19087, 70051, 10951669, 25632109, 12957651503
regulator: 344440752503954849477393804.03600963081150127841276591289492262257238204921428879
submitted by: wgxli
submitted at: 2026-10-09 05:01:21 UTC
last updated: 2026-10-09 05:01:21 UTC

Witness: 21 independent points log in to add more points →

(15115124808991170813219902, 53711907146563629845147639117194400443349)
(-153356177456177800901422798, 71396798441537760725441953005584460436049)
(-3614759131402429439091802948, 58324108757739791542867248449611090507349)
(-3704834662933476440533993888, 31096070476442726985289280818841328078269)
(-3733648014886593557131339198, 12258818387232946881264108485070085840349)
(5582310909309738972314598662, 321883114842759811602910539404277061517669)
(-2868715243979143058113481858, 131194284841052342478755286795159572195629)
(-2906429505353508358225541138, 129478352034930676446119159762021041667869)
(-3166509717062908418341473298, 113962794944016444123293941923152340683549)
(11102575703177509884885286862, 1107076790048544566352095781202242852834869)
(14267383068870755005420906496, 1649135409903455360326794530601639343284605)
(20633248958286079573816868702, 2918197749707487726192509093714092476353549)
(35661617936838447067556929286, 6699751756014617054168893192811960806603109)
(-57890715982699707466597827058/121, 128134801457298081815172089469593513600948719/1331)
(-1883646492374956959849414986746/529, 840882952932332299813611248108827631811303235/12167)
(-3775661855718563986826334301186/2209, 14892080066373167686216587914590749991091561827/103823)
(2373635060407499964838443506108/10609, 13465492809059339249680042576846405053903061763/1092727)
(40164426618486498416063374661807/8836, 160218016996319808583020674383293926531846553071/830584)
(-36450114584588157519404545495198/10201, 68850747419620319293071287924017046855038597549/1030301)
(-64717573897152165730295012336134/19321, 262642227942185320329230494006772291414146433495/2685619)
(241887064169125584604161971050586/42025, 2960068275789137988362730085679304783038340277469/8615125)

Commentary

2-isogenous to curve #4076

last edited by wgxli at 2026-10-09 05:01:21 UTC · history