curve #574

← home · all curves · JSON ↓

y² + xy + y = x³ + x² − 606809153046647289572228004472735x + 5705914512356054064577023265412257153734848708165

a-invariants

[1, 1, 1, -606809153046647289572228004472735, 5705914512356054064577023265412257153734848708165]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

493924645235645064336959943205775003527161188762990750217492804356802825836265486325169790

naive height

238.0709 ★ record for rank ≥ 23

Faltings height

17.6962 ★ record for rank ≥ 23

discriminant (Δ)

235187159075404753834686846556861825679493071641385675623561373722535233550196173968592847206400000 ★ record for rank ≥ 23

primes of bad reduction

2, 3, 5, 31, 4589933, 649632216244787, 2349379863779204533773121163, 75814208565514864645004430940635026011

regulator

261229837681060974701096889.881477733683333029439212415991271039797360029392866716154

submitted by

Jason Ma

submitted at

2026-09-04 17:09:09 UTC

later contributions

primes of bad reduction recorded · TristanPhillips · 2026-09-05 11:08:42 UTC

Witness: 23 independent points log in to add more points →

(-31874006875732275005397/1957201, 9191660792885048075918337538841902/2738124199)
(-13086336220921427, -3377241367674247055260472)
(-4676733905509502307625167/165611161, -1209798472718427335996821916227557868/2131250030909)
(226923720347930931951887/14799409, -4604519244067234688667852448438266/56933326423)
(2132819200717575608835/137641, 7867692179966855967122168752214/51064811)
(-10020903775029477, -3283352914516507414107422)
(-27614171516664917, -1185524354199834403307582)
(-10240086827525438585212096997/697894830801, -1972871141572528378248719320667702756057102/583022039545986201)
(17594638774362235, 690016003499161766941474)
(-90391391853372738850237/6558721, 56839901561376991941009874417600338/16796884481)
(136785257701458479423/6241, -844606886836652052099738841878/493039)
(38267170206790038211548283/1995498241, -94400737863047499764908787279454413922/89140901923711)
(129990948733678137683448403/15900957801, -2278739159684512766219595043171585584298/2005094877748299)
(-6657795774848285647/361, 22356722070735645892565057052/6859)
(16317685569990123, 386073158047419485106898)
(42324043977659502689621783/1909165636, -148024269480121202442908786873545387443/83419083299384)
(-30895692796644410941067093/2553988369, -433421719923693306324390103440288687406/129070910204153)
(134178150789577347945906427/8404672329, -227712025107052525125144176476073720846/770515145105733)
(11309821650737681184531211/708358225, -5579387613120624446977834063623011986/18852954158375)
(70571248468232136366667/3771364, 6960781075573079950290651382879299/7323988888)
(15537039146510534843854843/1016908321, 1168833209443705603748686636445181762/32428189448369)
(-739761539734064327707724601677/58595519062441, -1511408047233546424169155383451140608829893322/448535280049120556011)
(36293949457724703377/2209, 42963424005670654924804810254/103823)

Commentary

No commentary yet.