curve #6255

y² + y = x³ − x² − 544143984078270x + 4721760020722838931056

a-invariants: [0, -1, 1, -544143984078270, 4721760020722838931056]
c-invariants: [26118911235756976, -4079600501191065421890776]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 362690224994678250876232239094171126809255
discriminant (Δ): 680044171865021720392935448301570862767353125
Faltings height: 7.3706
naive height: 113.4043
primes of bad reduction: 3, 5, 10433, 565163, 10754417, 11452501, 33294649870321919
regulator: 52408437985889.07597862689710322924387138309710369136141404706735957405
submitted by: The Wren
submitted at: 2026-10-31 23:03:02 UTC
last updated: 2026-10-31 23:03:02 UTC

Witness: 16 independent points log in to add more points →

(1991701215, 88880527524412)
(869137530, -25614025752233)
(2348089017/16, 112421038730875/64)
(347317693/9, -5480026630217/27)
(3688138185/169, -125059899318011/2197)
(76584905010/4489, 6045674287593256/300763)
(10928859860/961, 62126039990057/29791)
(1249635590/121, -18991870328528/1331)
(112962573315/14641, -55535375691939368/1771561)
(-25205085, 49236747112)
(-10464710, 96281238487)
(5262090, 44767516087)
(10509242, 12802483415)
(15495990, 3270410512)
(20351990, 45576442512)
(125117295, 1376687431852)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 16 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_16.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 23:03:02 UTC · history