curve #6424

y² + xy = x³ − x² − 21722846736349x + 41413442684837140129

a-invariants: [1, -1, 0, -21722846736349, 41413442684837140129]
c-invariants: [1042696643344761, -35781209787564394020045]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 42435821077750672948299915694730546374774
discriminant (Δ): -84871642155501345896599831389461092749548 ★ record for rank ≥ 16
Faltings height: 6.6021 ★ record for rank ≥ 16
naive height: 103.8634 ★ record for rank ≥ 16
primes of bad reduction: 2, 20587717, 5224197837395591, 197276252379186121
regulator: 8388559731573.460738717631140529940496467948014858882585421561429252913
submitted by: apkorte
submitted at: 2026-11-02 16:10:41 UTC
last updated: 2026-11-02 16:10:41 UTC

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

(2567252, -1603037795)
(2799030, -1595052743)
(2393412, -1770995537)
(2296600, 1906171977)
(2973352, -1765188007)
(2189558, 2083876897)
(1779884, -2897084417)
(3475120, 2807368833)
(1264096, 3996069809)
(1241488, -4045158303)
(4128440, -4702826007)
(2384225, -1782899148)
(2883777, 1657343755)
(2917885, -1696066513)
(3006927, 1810093268)
(1886937, 2671563763)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-16-m10-160536.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 16:10:41 UTC · history