curve #6217

y² + y = x³ − 6042362262997633

a-invariants: [0, 0, 1, 0, -6042362262997633]
c-invariants: [0, 5220600995229954696]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 7211879845392172563924114983481
discriminant (Δ): -15772381221872681397302039468872947
Faltings height: 5.2408
naive height: 86.1983
primes of bad reduction: 3, 281947, 3174939899
regulator: 4571365706613629.51611767829853559560196403457207138423196959
submitted by: jesper-petersen
submitted at: 2026-10-30 22:11:25 UTC
last updated: 2026-10-30 22:11:25 UTC

Witness: 11 independent points log in to add more points →

(677584139711217/3617541316, 5003909887266235053869/217580639992136)
(62960864649984753/127193516164, -15399596372407163329371925/45362549991761288)
(1152472778276217/4045468816, -33625254418912127617619/257307998572864)
(1270250924930385/5201005924, -34633795269667336441133/375086145227032)
(1845722764659577/9667608976, -28777946550718819354349/950557984956224)
(18026376852831225/66454652944, 2020983147300732024338221/17131212073127872)
(21016149473205625/73977472144, 2614595083851241563601171/20120984693502272)
(218313266354425631321169/23653563348122500, 102004309994774639654245616802582053/3637850630285698350875000)
(191943330556186831425/782094023811136, 2044761962630111358279605970529/21871997672636895952384)
(218022380647051137441/573073231346704, 3037469739017867806161807745519/13718770285400717027392)
(30712046503961381662961353/1614266179257213504, -170201328075257081211011711792386381445/2050986122523089075156203008)

Commentary

Generic-rank-4 Burkhardt fibration associated with quartic coordinates (8, 13, 31, 16, -14), specialized at t=8364/10145. PARI/GP 2.17.4 returned rank bounds [11,11].

last edited by jesper-petersen at 2026-10-30 22:11:25 UTC · history