curve #722

y² + xy = x³ − 5152250234687087449326702539207922184750778638927395x + 111531423513419953826018835010907912192852206090701385211981956292110433537025

a-invariants

[1, 0, 0, -5152250234687087449326702539207922184750778638927395, 111531423513419953826018835010907912192852206090701385211981956292110433537025]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

795782071059399763647622054740486313091706224422174171987194937470243868084336258018666123658142342669282867802274273452084481310

naive height

368.8274

Faltings height

28.7482

discriminant (Δ)

3379520280513602230749292511273422593149788860757998199605856878800282621524333775998784986989220586181759399102334136596686153666040194913464473452108800000

primes of bad reduction

2, 3, 5, 11, 17, 31, 73, 79, 89, 107, 137, 1571, 1237185802217549359761415588722997437656534470665026779, 1673295230905984962861714833270310297778055365086240131

regulator

1251024572587769594948059615120463.796509358354234326289896918872746534711353540357000656850576

submitted by

FNacc

submitted at

2026-09-12 14:57:14 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-12 18:10:30 UTC

Witness: 28 independent points log in to add more points →

(23685362389927017719345790, 52781743191999446537263524856130989305)
(96948421353942845493101775/4, -239141258817762400857355942904862909735/8)
(24360034968351859146987990, 21862015883704034441352291858361810905)
(24501230174190295178915250, -1815198537456643429196131341728669955)
(22616097357181357598821350, -81089394056682741133186411539716570055)
(24455426282634624120178620, -12528069693066307738754541491161609095)
(-315878001675937086451735725/4, -1288319806278603244388094641269847087565/8)
(19115106960663991798871790, -141527477122645560143324766284505835095)
(-63483097805840677258604610, 427514632827280704462032819954779600905)
(21433362043926961501343640, -104630921962759106852809521673307250345)
(-80708512054264141052593050, 40467383649534155626252844387924292705)
(131258315070934906703740360/9, 5365584158501361142464088368272435227435/27)
(18868674755083523892064590, 145027739117106004147251758942185478505)
(76750032413008445617611990, -410118636090930626558335875460016057895)
(99886205108796626034968430, 770378307309505836509019785968136251305)
(20768581712769965330976840, 116123592137399298282607263466353275655)
(215879616771091191390815620/9, 1128597816157184742310673189919864099155/27)
(-10460997557927575234195830, 405320031377506471523324462777599392405)
(8827604142565075137474628340/121, 468601660835776061182422352014929537357305/1331)
(1440860595713603555316928374/25, 9706844097805931928632748633824008064733/125)
(72888992337473588341522830, -351047166972498870479313517917364794135)
(5997214785467836791609990, 284337777236801926488096266434415199105)
(8832044898996393017639180190/361, -76112512921330359798185805038898165916605/6859)
(375907506111960641028301710, -7161907447640402864370733646223893687415)
(13613228763050158911807390, -209560172605655044887328157810786138295)
(8512970277151335081113733540, 785427813455256093552920232327767653701555)
(112870675285791018314788144335/4, -37920170467382686113003013514235870935306535/8)
(63880839297992966247033090, 207566452276021465940132211021537347505)

Commentary

log conductor at most 296.1, exact value needs factoring of n = 2070177102595220499053437972376694473768587201128907747927146438037683428929547177088966432025786901539468049 factored discriminant: https://factordb.com/index.php?id=1100000009156618230

last edited by Maksym Voznyy at 2026-09-12 18:32:49 UTC · history