curve #5619

y² = x³ − 28562949550352379279676163362992675

a-invariants: [0, 0, 0, 0, -28562949550352379279676163362992675]
c-invariants: [0, 24678388411504455697640205145625671200]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 114251798201409517118704653451970700
discriminant (Δ): -352443781590901280211960875565870329310001133079319004437516268779230000
Faltings height: 12.4075
naive height: 172.1980
primes of bad reduction: 2, 3, 5, 7, 17, 29, 53, 103, 1289, 89293
regulator: 3310858328412.07841935711740292048354824155028112639436
submitted by: Maksym Voznyy
submitted at: 2026-10-23 23:38:56 UTC
last updated: 2026-10-23 23:38:56 UTC

(621006437701219417127307564220419635285901253729/234256995912506683737041100040550596, 489002379878818263425085709369585744603241868416566146352972549084125617/113380627033248324256356295249877836948032189965148856)
(175499996620800774557039100938064907553239/573526054230185067770936895201, -4124354378499365391517432554420917722908657528644440553458162/434339900800884472349631383575976620152298449)
(57675223036369/4, 438007810581053701703/8)
(196715883777888275498165865880520224005571/31948391318294493747849818025, 87243397771896189033521282218009600738657360993626429396006244/5710491544877888963694193608279894820528875)
(157866283108915978180397822814414687961/103981293521641143212144400, 1975397187398282780716063180381213694973139317639219743459/1060309917600770902804731900712144872000)
(13374468248929331680885271513674009/12693236181217992767236, 1527731100648316534938079313541097476645450129081827/1430074100787342632669081720395016)
(402155910902905223075604756748831/764783763664384605625, 7229364771203161203455660744604846407221293266146/21149883961178567173237067921875)
(1561091280002831022219141052795762232239/948549524456996135609182569, 61481799201192184201645902617911320616841337807524219879938/29213932129579869260067307541602044972747)

Voznyy (2023), A = -65050350356732790, [r, s, t] = [14, 85, 424] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-23 23:38:56 UTC · history