curve #6407

y² + xy + y = x³ − x² − 59051671710463557260462130512x + 5526977644249172256657295076289629805678899

a-invariants: [1, -1, 1, -59051671710463557260462130512, 5526977644249172256657295076289629805678899]
c-invariants: [2834480242102250748502182264561, -4775308684631272074590813485785871892286378441]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 334235773913133761458112380342418823690
discriminant (Δ): -17691026940636052146602698944688167830367045574862618307314666968551018927144000000000
Faltings height: 15.2890
naive height: 210.3596
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 47, 223, 227, 1621, 4337, 56614249, 45032942593
regulator: 16274844301585.9243819960700268043585847557615577755069837641
submitted by: Maksym Voznyy
submitted at: 2026-11-02 02:00:30 UTC
last updated: 2026-11-02 02:00:30 UTC

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

(46114658507776560968017779157/398078273706201, 3897598804846073188694136915796713046322579/7942417511080478025699)
(101638944015757, -758291982320924012879)
(88622885857857, -994833516291249838379)
(38984666973079042657/1681, -243397995744110474226244005699/68921)
(638725742988825306427197/4526463841, 19218488363839242209177352413638879/304535960758639)
(12972396786254857393/121801, 28382308778413559056435979037/42508549)
(-21467281455490599671079778563/446177791572241, -27081184324621105486458674340171144106541719/9424578243334912435961)
(123201622200649637014212191973/2117349579120889, 147371255207775621698755704776560403154507523/97429135805837860078963)
(1214718229491930549862861177/3583104482281, 33551283020448084090782674435432797639069/6782490722450045429)
(-2495055794485786695108739508403/68821415652166321, 49838882859215360881315850743560197428845444601/18054497383889058750539881)
(245906549135073748063360634564577/1297564600252238761, -1579771274421694955189340381424619065556794119089/1478064829567569520921952491)

Commentary

Voznyy (2026), t = 1095/689 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec

last edited by Maksym Voznyy at 2026-11-02 02:00:31 UTC · history