curve #3540

← home · all curves · JSON ↓

y² + xy + y = x³ − 16028688748570897897112037408119359x + 932007813775619598336216026466387194695234595603846

a-invariants: [1, 0, 1, -16028688748570897897112037408119359, 932007813775619598336216026466387194695234595603846]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 28831589945032470081808355979517424400977899692664321348218816633405655377304892986208070
discriminant (Δ): -111695220780561162296794795842875902889146377153148165465181368356712565990564097557513974494691867971300
Faltings height: 18.6832
naive height: 248.2460
primes of bad reduction: 2, 3, 5, 7, 19, 23, 61, 3169, 101917911569, 15946496096540764315950758636424701502600885274911006907756160606971
regulator: 2116468695862981109474041674970.6264138412292839761151495446453913977381401821047625625
submitted by: Matej Jurasić
submitted at: 2026-09-28 00:25:25 UTC
last updated: 2026-09-28 00:25:25 UTC

Witness: 24 independent points log in to add more points →

(615998849276675119, 474132829229335094405291318)
(922211486934096733, 877762543527632725188551918)
(240137638793630140, -104550054978388067192156938)
(188168674549348267/4, 134363384583707900181097339/8)
(-1229454777128194184/9, -645964847609306796002673554/27)
(44746342342328623, -17446355496803150375232742)
(77665055145420274, -12474118009715070515321152)
(-3649775288731905314/25, 1583563317224018254937645044/125)
(-3851794881963542063/64, -20977550618406604515062387459/512)
(-54059319847225067, 40503386617303771867571318)
(-18115636196053841, -34877393612631861602031142)
(10597093512144394, 27628614451087827169737512)
(127497075539213173, -30998808582445463767790092)
(73236869589211933, 12285477613867423513254068)
(42765029372758783, -18020854491637290994698802)
(2835310639353258138463/961, 150837264144849496204252370413118/29791)
(289394453943023149, 143282705408287508529253598)
(15447405222897544277719315970635759/872786038565134225, -20849919651065817142372245144290072165176998713487518/815383062274122481571581625)
(762483637557163958567169514465/6051299883721, 449757198299090171675010983913766590931443598/14885828584660753019)
(-5430534947568799483679006658353/392044831214884, 263397888936259513337155137639206721207661549429/7762535487524111415848)
(8400526457958580116701979294121/3942988604416, 24305949176581562618691534875049806128676407237/7829576699834433536)
(137268620985763613516944565668831/2790069133421025, 2387742867655179168548870945282835194516124920114/147374534653690970732625)
(3117190030164005811564369397/20037251809, -133142169307842583705731653611760469993514/2836333105319377)
(-836233251220185765494891576/67112601721, 584393792017659269676708243262312657571833/17386257714443981)

Commentary

Specialization at T = 121 of the rank-17 fibration of X1008 (equations as in curve#751).

last edited by Matej Jurasić at 2026-09-28 00:29:01 UTC · history