curve #6409

y² + y = x³ − 21294602880082567x + 1200784457206576912061316

a-invariants: [0, 0, 1, -21294602880082567, 1200784457206576912061316]
c-invariants: [1022140938243963216, -1037477771026482452020977240]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 4893398869845545444651931147962802770642897837243 ★ record for rank ≥ 18
discriminant (Δ): -4893398869845545444651931147962802770642897837243 ★ record for rank ≥ 18
Faltings height: 8.1938 ★ record for rank ≥ 18
naive height: 124.4132 ★ record for rank ≥ 18
primes of bad reduction: 5261, 426410096279, 2181297172636373243240166679877297
regulator: 3252620319985860.3079538903956226712585838937812227751689681047553287801112
submitted by: apkorte
submitted at: 2026-11-02 05:34:39 UTC
last updated: 2026-11-02 05:34:39 UTC

Witness: 18 independent points log in to add more points →

(83266954, -70495680222)
(82697277, -73021907035)
(86591938, 78256331418)
(87335357, 84617107034)
(87719258, -88364474382)
(89489184, 108652251156)
(78314673, 115858574181)
(74291162, 169734260109)
(96127702, -205072233535)
(99182197, -253781328891)
(100373458, 273161422506)
(48912548, -525577186057)
(119225187, -597222890266)
(132334869, -836828949627)
(14221714, -949112821867)
(146676053, 1110380515706)
(-104222599, -1512633779526)
(-125949548, -1372900590216)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-18-m10-051720.ec), where it is recorded as a find of that challenge; not our discovery. Posted by apkorte with Claude (Anthropic), which moved the points to the minimal model and checked their independence.

last edited by apkorte at 2026-11-02 05:34:39 UTC · history