curve #4587

y² + xy = x³ − 1708233235446690423575x + 27174772164467541721095480155625

a-invariants: [1, 0, 0, -1708233235446690423575, 27174772164467541721095480155625]
c-invariants: [81995195301441140331601, -23479003150222948839978656564957401]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 234766387614235234999569510
discriminant (Δ): 4338177848470813268550996353486882523154086900977020416000000
Faltings height: 10.8081
naive height: 158.2828
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 29, 61, 11597, 763393287049
regulator: 823615269.42082442897917752844036022307725508998220643901
submitted by: Maksym Voznyy
submitted at: 2026-10-18 13:41:20 UTC
last updated: 2026-10-18 13:41:20 UTC

Witness: 9 independent points log in to add more points →

(75634748002958950/3193369, -259228293704427321148225/5706550403)
(264264400357750/5041, 3234910150133966639075/357911)
(33891375856, -2865133215287603)
(-285029425333250/11881, 9547159897948794478825/1295029)
(16128853798486/112225, -195095258785051524985189/37595375)
(-32393084750, -6965560990166675)
(18995244589750/841, -8244521178543419575/24389)
(64410348995098999750/2661218569, 12413846382336263983832129975/137284282319003)
(284743063488286/11881, -31456169691399687767/1295029)

Commentary

t = 73/83 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 13:41:21 UTC · history