curve #1933

y² + xy + y = x³ + x² − 178794778214407978859461188x + 919419935068616719030140166742670899781

a-invariants: [1, 1, 1, -178794778214407978859461188, 919419935068616719030140166742670899781]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/4ℤ
conductor (N): 4730660125828472197497334873350
discriminant (Δ): 616781387570173366324240409153518432934577473773872985690607451726151680000000
Faltings height: 13.8471
naive height: 192.9584
primes of bad reduction: 2, 3, 5, 19, 23, 31, 41, 47, 61, 109, 157, 193, 233, 593, 5749, 7549
regulator: 48272515.12524590485317643502214131261486922660304121705781
submitted by: dujella
submitted at: 2026-09-25 19:20:54 UTC
last updated: 2026-09-25 19:20:54 UTC

(7991223717565, 973476603398652017)
(7157502138095, 2524594321090659027)
(6490090505595, 5691791551237981527)
(8260503930845, 2479531125255223377)
(7068765426045, 2961370070561940177)
(7986191049565, 940173095443704017)
(7906176561445, 182183392974586577)
(7447027420345, 963938571466557377)
(7536040864245, 36725312300251577)
(5577275134045, 9783604580829236177)

found by Elkies (2005)

last edited by dujella at 2026-09-25 19:20:54 UTC · history