curve #4589

y² + xy + y = x³ − x² − 35462620498211018636297x + 2570404889564486437438128707183369

a-invariants: [1, -1, 1, -35462620498211018636297, 2570404889564486437438128707183369]
c-invariants: [1702205783914128894542241, -2220829824576056355918929622980990961]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 31530318364132052094720090
discriminant (Δ): 36956888212049200929714493783423906963826670142242688301568000000
Faltings height: 11.5650
naive height: 167.3819
primes of bad reduction: 2, 3, 5, 7, 11, 13, 37, 71, 199, 6229, 60133, 1787341
regulator: 15994162.276478232068180408504337244172019564149461881302
submitted by: Maksym Voznyy
submitted at: 2026-10-18 14:18:07 UTC
last updated: 2026-10-18 14:18:07 UTC

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

(14640832981264483/94249, -823567921457363851825752/28934443)
(156318009127, 29096987433463036)
(52163700808457094114097/478298111281, -47367281090654290490100079656494/330786669078938071)
(44738516786429767/408321, 121207709653150188657284/260917119)
(4106700030685865026052527/36901967940601, -328145509176871381615595310067468236/224168347746800954099)
(764507765426317647/1038361, -648444523465840997751748876/1058089859)
(21312444111899410498982583/194773648313689, 1025985769704514280383589437934487532/2718286940761069404637)
(8732035208354703/80089, -2662850079489084047468/22665187)
(2711782888029279183/23785129, -352834354780892473531991812/116000074133)

Commentary

t = 495/97 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 14:18:07 UTC · history