curve #3837

y² + xy = x³ − 139713739832512991882723203912729789084668247729170106340x + 635799737439486793982215335832203794939131215639703128605804098076829141464016978192

a-invariants: [1, 0, 0, -139713739832512991882723203912729789084668247729170106340, 635799737439486793982215335832203794939131215639703128605804098076829141464016978192]
rank (lower bound): ≥ 30
torsion subgroup: trivial
conductor (N): 300337324243148559564670083565652945228316286138687422216882058213198178245647501856761588327235374008793884512293657719156250182670
discriminant (Δ): -91297332450483867319008082917355533796049750077401214821259820224465235142369674552146868945077556682912604706171512084822337748466727586512999082821770690928640000000
Faltings height: 31.0143
naive height: 399.4517
primes of bad reduction: 2, 3, 5, 7, 13, 29, 31, 37, 41, 47, 79, 577, 2480768272566289505656531, 15177995732504336989633137999948066650079622020804940687380810831517943179379482185720186223
regulator: 67106621786466148040820163102726372.372860823376546962664732100971880632594466991825096978429478549
submitted by: Matej Jurasić
submitted at: 2026-10-03 16:43:42 UTC
last updated: 2026-10-03 16:43:42 UTC

Witness: 30 independent points log in to add more points →

(-2214949464343802059485021176, 966639574023799304838642057151532993146588)
(6412510334541751949855827624, 59734526993303348414283492965199212736988)
(-2827995043783074849568836536, 1004137666157041179294127701688616751864028)
(6929160737352739609857331432, 19809897836368385861578994886729387124540)
(-9380612496345857979231429176, 1058746824456207729252780506438744057866588)
(6825615853219223607051895624, -12893944338805995918589146338960910719012)
(5851712607904221660540055624, -136427967131941974413715091975580905439012)
(4070992206904974461303090824, -366735127618926604503365851192874213677412)
(6699895156650630821560275784, -21936489809627729486515824187736040482852)
(6887520233935421077664023864, -15756407141801668462400553973112361585572)
(11537239111738450562090234284, -748055095527718687850588900453636712356852)
(7798008760021353493376585608, -143176192096546067336655768285067127263844)
(3562326391442021481687740824, -428135866127319251686079161878397519477412)
(878775230880551411179042504, -716729651985800572870492882692434166484772)
(4705428481712228359919417224, -287349765778085409488438628929437863066212)
(535491455052138159167413502344/81, -24046308238361092913440900472803652969530948/729)
(5890439915276481967149570784, 131173948600578897574823090540020069662148)
(-12671297128785173149686222392, 609613107556164163263206514165351610177756)
(6181366131168678980677176142984/841, -1884364509555087004063911303407831524273881268/24389)
(423038827425071820637254150376/49, -92733499481725867881043277565815018333152316/343)
(6383131941300318312709106824, 63759024667126846836274156026904574482588)
(7098665464068522073333135024, -41567459608248174694923293067465922386212)
(8058700213142889470869829704, 182323703397052094291366636081992592068828)
(6541225989303727169990054824, 42239761460291493833214431285698866430588)
(13408139153730241371636733054, -1083046414069959093098914807212045068495432)
(104785336130815902425381127900904/7921, -740254501170302544300081951214882754595304432228/704969)
(149896123072939809940458106984, -57859194721204718626357404969423549230091332)
(-89121076136835769028067071084/9, -27644429944453573587248587672359131944642624/27)
(-8007934274128188457507846316, 1114043666654887640249819832271092031704268)
(-81180900368265661612237171404536/32041, 5658898926510620450937286520439598391261226331892/5735339)

Commentary

Specialization at T = -20614/15737 of a rank-16 fibration of X1092 (three neighbour steps from the one in curve#1879).

last edited by Matej Jurasić at 2026-10-03 16:43:43 UTC · history