curve #1892

y² + xy = x³ − 48475969531027158606349900914146476669312780x + 138322764403644162134777583174569810494507496489970692704187499152

a-invariants: [1, 0, 0, -48475969531027158606349900914146476669312780, 138322764403644162134777583174569810494507496489970692704187499152]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 10851470963463010575883593795717559533867309643030787483861715880289147049155818439922373473127890
discriminant (Δ): -975000402090640692321997253529449506746170150020686691597984885743246035272081960473306496915892726837942677247251542936902860800000
Faltings height: 24.0739
naive height: 313.5080
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 43, 67, 1307, 9923, 490057, 1551733, 1711896451307544529499256285057620689633205721825977557550991665807
regulator: 105971873086180401474068548.9507613028995272982223300550836523938766996518703310087360581
submitted by: Ritik Jain
submitted at: 2026-09-25 17:37:07 UTC
last updated: 2026-09-25 17:37:07 UTC

Witness: 25 independent points log in to add more points →

(-575459824839025592820197289597245370264926552221/3440877881608009017626157316, -77234611911573750641124798051753627837772144768943884699722324402183634267/201838443943277821201180830807564836646136)
(-826445232101792840052584/225, -1743355058680804601840318335896464884/3375)
(172811626561316349779804, -71781495077020198742248285786937692)
(-24495481899481875533052056/6561, 274743404405992487362489478309697387508/531441)
(16867595432921652796459504/225, 68987519766673867345674905705025999628/3375)
(3487871255515281230051/4, -2487939043054739603378397786006101/8)
(1131619071707004339092384/1681, -22438488704383752738160292192047536692/68921)
(10321689233725420408765384/361, 32263686635762902356626733182715304252/6859)
(-465514691864411490933722/1369, 19927125361285725705866332976682492784/50653)
(6750713201729948298584, -344557350797120292185183829183052)
(14222522405047051185700184/361, 52854436932176476803541781948658411452/6859)
(292799254460532959762968, -158392031359377982999024288718532044)
(6954884662228844851624, 370929486844821937081517848329508)
(4654269490724669508884, -116294320318420136854678036456732)
(44890283421802550244668024/5041, -229958521563897581334799989032833587572/357911)
(8000439471782077769063983064/534361, -649960485820985729538738926828501051433572/390617891)
(4898142916687494458724175646618984/1092758713201, -120315999876797712776626492890917725220376425430532/1142316413603378551)
(122120591048695956373485390104/20151121, 23435197993217003696309955485667030473039252/90458382169)
(630398960201874691444741742906226746/532508375756449, 3531550559884560971829500620672673470411117542811423066/12288239427653550296207)
(1396792040688598632077021438192823544/202445915265801, 1047747638088049954307996916273662415537038916765158372/2880471136026244392549)
(12068430301236321225781955656693958041534492/697025255516177128641, 38991541552956064309405402197744381746791840541510119433535908060/18402328178926636229466550681311)
(96033440944738224072750585771776346411865103/3634129969820825376196, 911491913837662846014943411967745479198277146181163289895722087311/219078966163723498001049866851256)
(121237907157935470068396453252120588939014/26666029291610398561, 15025423834747413740634610981302502288180241496743887866231728/137701137475363975515967159441)
(-1228127176241993231532233918857615897889021419/167563436623806593319184, 21679038697479650787590363065527127590814591538393130989107081151311/68591276987299458535894321233714752)
(-2159910501599112698050424/729, 9957735599999111986250998638582934924/19683)

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