curve #1899

y² + y = x³ − x² − 987976885369910835971705211159445595981260x + 384845024024579580196957879976067543042479368580733836795492748

a-invariants

[0, -1, 1, -987976885369910835971705211159445595981260, 384845024024579580196957879976067543042479368580733836795492748]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

27669798401641859725876449579856058574725213628931780556545210180466419464223473796059698255427074599305

discriminant (Δ)

-2262453793602840312394581890850668082657288345762664782987971970610072503862914626455019993249661202178704268468297700036796875

Faltings height

23.0356

naive height

301.7390

primes of bad reduction

3, 5, 7, 11, 29, 37, 41, 61, 593, 733070621588840725846204446095260985734459, 20535727296801213165057340241181092541685319624581

regulator

22564467310982597752934752068.4975314922832898464282835248111789339945939344886630159423414

submitted by

Ritik Jain

submitted at

2026-09-25 17:48:18 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:50:48 UTC

Witness: 26 independent points log in to add more points →

(56305012552990793114372601/73984, 172803437978643973455403333286993109901/20123648)
(2657914651112031170261359/3481, -1786099085775395292831099463854568402/205379)
(36006896371527288414, 18690043486140694520109802136487)
(-8345912523050179885529/9, -605899956975211834133257481010641/27)
(155213503763973878603946/289, 14858783831025013461688683838224856/4913)
(83031732388722215213701/4, 23898852675447725683272016013489231/8)
(733325332892450899387, -7395539791243861464991471877522)
(11735601594659193942908031/15625, 15926583593797641751678409588279039929/1953125)
(426657032251008305837949/676, -62640889200068132025294043174824173/17576)
(302971959255327064479789/676, -99542960225480439531399231818741013/17576)
(55678668399630037805041/144, -13456588109787300582323346274927489/1728)
(-1148260922986791420446, 2305348884017200078647356598727)
(19771479670237863459384, 2776643304997742081784773684062307)
(146063390782350842976038407/25281, -1740740872490153008129658585749012137701/4019679)
(163779967147543821325746361/222784, 785798566747302438008530075737789830131/105154048)
(6267397267084671405950803884514208581/8005957797136324, 6839954938011231332327718577074037265032103995812421999/716341223963810074677832)
(335366798547997732224680832303241653609376771546/135692056773633455049735225, -180498913072930293226990751626982184604211511116715097385305242783610981/1580635159452657130710586860417375334125)
(-3977453432843911974322898197576266/22749475268881, 2549877398805267468589498422694024665937807670824527/108506829970940841721)
(-826459392647519843079411888467711593955646162077411891207/2568871512162977805810182010862951441, 106526059694966647871617844301519242351508032895922523853509488555740463880400037826623/4117310064737223451666318552940713353187741707793690489)
(3438555953071159898780699230975292824893300333450041866/5697427785802215893494901496934569, 1246844536471636101794973914921846692989501052916575147760112670239231656001586061/430049298806092711885296312286824026674604062257003)
(-12131431273488563083105613774/11539609, 634032518083274557354784297241861411465451/39200051773)
(96481748553573255264729127529003761/207487978140249, 15234019486921932255579859451628072845935772826639784/2988748754306462726307)
(-1305611734841981173988176761603395369042156424/1211311894606812293014225, 18737202072780318356691867767261431486005490284868349004114764930876/1333165212722803652393637376498281625)
(39180476194172978602774838947448870191645602/64193383942021243876201, 49346411338698160943070579029041472529115305270589776083865686488/16264301073289866500419371330229301)
(-1030147827208400530536, 17590045725798988309505573680412)
(583269490620141336339, 2649236509563140568802831271462)

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