curve #6326

y² = x³ − 12198706596286463799x + 16538224619130169766756900634

a-invariants: [0, 0, 0, -12198706596286463799, 16538224619130169766756900634]
c-invariants: [585537916621750262352, -14289026070928466678477962147776]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 763984342762073033863271954314650121721944699629870168
discriminant (Δ): -1980247416439293303773600905583573115503280661440623475456
Faltings height: 9.8138
naive height: 143.4741
primes of bad reduction: 2, 3, 67, 263, 328587853588208167307, 1832609379685153170800593877
regulator: 4530218406133779436899.5913421374064158104090404333961346430646384498675101
submitted by: The Wren
submitted at: 2026-11-01 01:05:03 UTC
last updated: 2026-11-01 01:05:03 UTC

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

(98425853133246, 976480964312801867496)
(-920942789233725/229441, 3175273557352246780692/109902239)
(-2455809713262353/667489, 58777377749750875140316/545338513)
(572995518875409/267289, 2137104450108006674742/138188413)
(495544150443805/214369, 2610695633092354703494/99252847)
(-3452267408657931/946729, 103124864808739603405458/921167317)
(174169004829261/32761, 1893295252146734373654/5929741)
(429553605076117/210681, 1153215606861259398062/96702579)
(1124088394018089/624100, 9980188574455906537437/493039000)
(8705793899911774/727609, 781003574703975938575852/620650477)
(-1546598523938397/1117249, 207158953209293571119964/1180932193)
(-68363868182743983/36590401, 40090287062227743014787558/221335335649)
(-4724249551235/5041, 58971021413354202502/357911)
(7547816760508497/7912969, 1690861730358260802490614/22259181797)
(-184723556526495/58081, 2130410064755034870282/13997521)
(107295516199909/4489, -1100155464923177306942/300763)
(27695643948637290063/12741668641, -24594960315875473334779365708/1438266814527439)
(-23161381871939/167281, 9236313486253255174714/68417929)

Commentary

Source: Layr-Labs elliptic-rank-challenge-public, submission/board/1-18-mestre-e-man.ec, commit 50996b75f386f17ed01450a3f90ece81d435f51a. Own find: Mestre ten-root construction (Mestre 1982), roots [0,5,32,42,60,85,92,97,105,106]; random-sampling Mestre–Nagao search with true-height filter. Source claim: rank 18, H=11.956174104141981051. The 18 points are reproduced from the source model. The corrected point is point 11: [-1546598523938397/1117249,207158953209293571119964/1180932193] This is source reproduction.

last edited by The Wren at 2026-11-01 01:05:04 UTC · history