curve #6378

y² + y = x³ − x² − 2164582322737751596x + 1226380924718007424155569076

a-invariants: [0, -1, 1, -2164582322737751596, 1226380924718007424155569076]
c-invariants: [103899951491412076624, -1059593118332958705521939222168]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 6155359341987891556276460466971039662842592963042515 ★ record for rank ≥ 19
discriminant (Δ): -646312730908728613409028349031959164598472261119464075 ★ record for rank ≥ 19
Faltings height: 9.2711 ★ record for rank ≥ 19
naive height: 138.2709 ★ record for rank ≥ 19
primes of bad reduction: 3, 5, 7, 1979, 755551, 14894974781, 771979522310093, 3409643562192599
regulator: 24121063400811601.74515872400313217251772307685224444906812877935051725959936
submitted by: apkorte
submitted at: 2026-11-01 20:51:45 UTC
last updated: 2026-11-01 20:51:45 UTC

Witness: 19 independent points log in to add more points →

(779978653, 3544849536292)
(855753589, -844003492445)
(394844704, 20815001115940)
(879342370, 1708013362912)
(-40110117, 36237246652022)
(57319831, -33203851579406)
(1620028720, 44401008037732)
(1221279194, -20109386288576)
(880372926, 1754992819455)
(2512751733, 107947392526172)
(-1120325456, 47384221944475)
(-1347661334, 41181237739519)
(-1539997499, 30126169352044)
(1079014970, -12125696652608)
(7088118508, 584808286582852)
(8777658082/9, -177000962359931/27)
(238017219, 26919458727425)
(-1692149902, -6627611784353)
(-1417423121, 38036584233109)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-19-m10-203427.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 2026-11-01 20:51:45 UTC · history