curve #1867

y² + xy + y = x³ − x² − 130924868361039507825398309492949976557x + 468543227146109554850832446149665186317119722112171421781

a-invariants

[1, -1, 1, -130924868361039507825398309492949976557, 468543227146109554850832446149665186317119722112171421781]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

29400846095027381788534438805700360448807640705300186835094975728508637215095251873217790

discriminant (Δ)

48792263346810280079539186453890932575581326850116570947177326323897981580751964246375041063856083815115490560000000

Faltings height

20.9151

naive height

274.9167

primes of bad reduction

2, 5, 7, 13, 23, 31, 53, 59, 179, 1129, 96457065549562880993, 57184279630354087610553286022312797213509481562710601

regulator

2763563799375720749835661.2552158151281076921945837990034807083413503613635817257460822

submitted by

Ritik Jain

submitted at

2026-09-25 17:20:59 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:25:02 UTC

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

(621433155691988900317319788716345994584164416890231/57772742692766774138784321625561, -7666459056236089164859116960499214924126305629025926570657807490390266221496/439121274709231143828834624633435960979734958691)
(31160951803346208876961/12321, -16949740916362099709018632767292076/1367631)
(62511102859438706352154771743911/1605869338441, -474452750799893193909342556224835060534788588424/2035004195883249989)
(1970938539950663684119/484, -18197050677857781190318419133883/10648)
(-1051545080722087051689/361, -197033046346170789656822642684344/6859)
(-250873790708535220651/25, -3472764047123751372628817718628/125)
(36100469848128363541099/3025, 4094793017003341376904297175750408/166375)
(80606778348880848119/25, -1117511410587303325444804658632/125)
(-10861161833105797037561/12769, 34728315289180315795720834126226168/1442897)
(1478391942949430073591, 56842268803264545367265356616504)
(-11705903781473744859, -19927328195419905211545570196)
(2018209808905440631, 14578404812900890337325611344)
(12698058530457077659, -29214642060303274634214960084)
(314559883818499399471/4, -5522326843548065988542163750177/8)
(14573697446883298071, -40691892743062143985960536016)
(-15819954967996521461141/1369, 1060513210610166123962699276454772/50653)
(132525115754200202218336719713519/10410702339844, -987761011725211879706807024598896115962748975073/33590776563051736328)
(1355262443732644025, 17134612041049984735619367692)
(-1427545996254150073989/169, 68487061864479898959374242736888/2197)
(-47826148769431937300089/3721, 1200999342737357863696856121287224/226981)
(176302311476335883641, 2336087256395216356922138386554)
(1687809978655274109301039/567009, 4379096678576895390352969887386519768/426957777)
(141314828001877353981/16, 69117562890834171618733634481/64)
(1331880790979855902359/25, 47549634105939135797980657660888/125)

Commentary

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