curve #6383

y² + xy = x³ − 101836384575389651594744209320x + 12510525671139513746635905975856139012558400

a-invariants: [1, 0, 0, -101836384575389651594744209320, 12510525671139513746635905975856139012558400]
c-invariants: [4888146459618703276547722047361, -10809094179864547209313112191194618928433528641]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 267933495334122942860610918833471852370
discriminant (Δ): -22722062486837669282133324357699987623337176872464040230881555609102226454216704000000
Faltings height: 15.3783
naive height: 211.9934
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 59, 67, 71, 543871, 1169473, 920442349
regulator: 311996546.349227689753927255732029634265039006611554394083721
submitted by: The Wren
submitted at: 2026-11-02 00:42:57 UTC
last updated: 2026-11-02 00:42:57 UTC

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

(-197905534774080, 4991314831998510048600)
(185210005353240, 51187058424127539480)
(184984155218730, 49054737516527065890)
(6940361502283440, 577592716080243047643480)
(400896883810290, 6009667566361600304730)
(185023231928220, -49389432498151330200)
(192071537178960, -190937606173232919720)
(200324619565392, -386274978884360402088)
(-368454071060208, 108720353923369918296)
(475615311704400, -8465488158680722455720)
(106308398308980, 1698794961469295263140)

Commentary

Z/3 K3 family y^2+(7t^2+309)xy-91(t^2-1)(t^2-25)(t^2-121)y=x^3, parameter t=1019/751. Family construction from the Layr Labs Elliptic Rank Challenge public repository, submission/board/3-r12-z3k3.ec (commit c8f82607a219df846ab80dd9e14ee09a2904d709). t selected by Mestre-Nagao sieve ordering; 11 points from specializing the family sections at t; PARI/GP 2.19 ellrank bounds [11,11]; torsion Z/3Z (elltors).

last edited by The Wren at 2026-11-02 00:42:57 UTC · history