curve #3927

y² + xy = x³ − 16867220517659124830933581618467435x + 842972955743914253841668451786117906973362978066225

a-invariants: [1, 0, 0, -16867220517659124830933581618467435, 842972955743914253841668451786117906973362978066225]
c-invariants: [809626584847637991884811917686436881, -728328633762741916533641419614662859452203489578873721]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 255374662650346705382646559358855732546892081330
discriminant (Δ): 141057280847071075368977210238323644732795927802564855019622262241059649506028059531092271784768000000
Faltings height: 18.3928
naive height: 248.0456
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 233, 241, 347, 647, 2143, 805038825809109964591466011
regulator: 23714389696169.1973930855798269556927448038840858555867320695
submitted by: Maksym Voznyy
submitted at: 2026-10-05 01:28:42 UTC
last updated: 2026-10-05 01:28:42 UTC

(192567760634774966499693746662530/317998662555289, 2615246597520590176269151723983138746355764280945/5670716555994454532413)
(1113102444534638917899750/14145121, 91400806835575262804926834387887585/53199800081)
(2143757136081440201265100433796866919634018830/28197817767221465071099919089, 1081420056123960028018168399138623179887298558085567598764072993945/4735035607731185485440352558207544650554313)
(857174166943916617830/6889, 14807065662888865722525580089555/571787)
(65297383585504177265970/687241, -5642930901479805881773822335316215/569722789)
(803185895984007826150/9, -22762693509038609790083464468445/27)
(76205244960120683362700220/999002449, 13687182840343989664347757799947348215/31575470405543)
(4109244085724195714058420/54007801, -113358067804425930995490842274682065/396903329549)
(6960237536129541779940054064629947666430/16855497150408936303769, 554860930673328673249292181563948687852491738430525302355955/2188327659830779443296176931486147)
(181723011883001298071822670/764356609, -2141666808423364829713388005456612939185/21132167169023)
(2392602259604898038733342809765550/31504547088011209, -693868101207349644884661759236397916166043263205/5591905980809608407730427)

Eroshkin - Voznyy (2026)

last edited by Maksym Voznyy at 2026-10-05 01:28:42 UTC · history