curve #4603

y² + xy = x³ − 287077106000101097618162595x + 1872044659794220981539436339856114465025

a-invariants: [1, 0, 0, -287077106000101097618162595, 1872044659794220981539436339856114465025]
c-invariants: [13779701088004852685671804561, -1617446586062227597601705004914711405488441]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 2889000441526096910007811045669530
discriminant (Δ): 207417342466629804899506932143657533855438663218711452803685924298432000000000
Faltings height: 13.8822
naive height: 194.3790
primes of bad reduction: 2, 3, 5, 7, 13, 23, 31, 43, 47, 67, 79, 109, 1272918873742049461
regulator: 81958694320.29007713465428635079100771450181598292096239128
submitted by: Maksym Voznyy
submitted at: 2026-10-18 23:10:05 UTC
last updated: 2026-10-18 23:10:05 UTC

Witness: 10 independent points log in to add more points →

(2436620372367049710/113569, 2861225865928978803735443865/38272753)
(1918123948757170477422/26306641, -81915635521696199926248275871231/134926761689)
(16243303107928421484782/1633857241, -52080517227954253338269862538043/66042143538461)
(130862110145735128633942590/13084287762841, 53810293217729788430456994316169176005/47328760465791484861)
(4375360860207390/121, 262082667717614008229355/1331)
(77695022367723353310/3052009, 560773009992183933595700219715/5331859723)
(195857538644245754/15625, -30451774495652721090159383/1953125)
(46030238964033242345090910/4418921107129, -32094129968902829398307625040928478165/9289115694481334867)
(74016844610810670, -20137049597830148069870295)
(1892053383193710/169, -17203443511131493004115/2197)

Commentary

t = 277/377 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 2026-10-18 23:10:05 UTC · history