curve #1898

y² + xy + y = x³ − x² − 61787833156199091907725540280512698498637x + 6322013642716470265366173743178457146053778170436012118524405

a-invariants: [1, -1, 1, -61787833156199091907725540280512698498637, 6322013642716470265366173743178457146053778170436012118524405]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 700151150909569096975323720836750387273516745952416992277408077136991450837720067763885946254140224374766323082222
discriminant (Δ): -2169176077592666721517381535400082025944988804163196579053549067375749377186822565419433215708874412641336192926217248872448
Faltings height: 22.4115
naive height: 293.5214
primes of bad reduction: 2, 17, 19, 29, 1163, 32135242120720043820039071728677678257863643342056794960987888323894409998003458463466856406679539914175491
regulator: 1648684221246040585277073356438.30325301569847671852452074738146127731459861409790267642601
submitted by: Ritik Jain
submitted at: 2026-09-25 17:48:15 UTC
last updated: 2026-09-25 17:48:15 UTC

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

(-178128570991374608273, 3417047015890764153761849976952)
(-2709663718713207264899801/15625, -6715394721202960328540729346479925832/1953125)
(150252253982126539383, -655978838608157072087926229328)
(1880248226964808089052487/529, 2572106003782796539136098748135523248/12167)
(310439279881521718219/4, -11297113356402766221560020983127/8)
(-37609866677589935127, -2931321643147255105262453742868)
(1038848614003716357574627/7569, -430344004133251429172996707093651384/658503)
(-1924771502941638576918905/7921, -1863574424451414147681275273037748840/704969)
(3012259989842837774289175/19881, -1856328136870823375211872628531614120/2803221)
(63720993787629774383, -1625903443075168571832914210056)
(355134193495983766437, 5400802785866689437950219123340)
(8136544101331532233585/64, -369761704041415860939566545799125/512)
(584921817053747239027147/169, -446228257543772939105506783166168232/2197)
(10156700958218048050959/49, -533625812161519782549358790177544/343)
(1368873410421791105554183/19881, -4337420225745106985975719224486644648/2803221)
(247094035846313054491327/169, -121164778087292440456166330408385032/2197)
(50590150767341580035805241959/364542649, 4510719077204746587158036730147858304470344/6960212797357)
(277960969704897585261734157992759290381/6162129380206414224, 29130670380691215863403411606101627204057279988620780117345/15296646090939761010216013632)
(-30102927183467385471539/144, 5492487828292632518040982834289615/1728)
(-6572811282817941689031493304842276875937638763361099/88590432671891556401067849738256, 2701657807436145013468019193495102524850604872895330296265035312722691654935321/833835218073646189558304906299892431167162716096)
(-4045194251709514910536708518381703023248317/21235757555395293876001, 10347093512183869995282325084143931787566789571643454986035058872/3094579453164246523127420706814001)
(-19064571302036057089352684596769/110267164225, 125974244218952485505326013282092505195890247784/36615865888374625)
(80697220544755429379388456707076678399541933/610912437837016719772944, 325645242774282065056820246984362213054564086148978911171048035885/477494584964521948387523630004967872)
(481261358382061672655480424247909242035286872254427/4652670623959482243994229704561, 10222473295170553468522487391555929134317178379654590788716022482291698789208/10035833857402197439783669610801694596241692809)
(890496572220388156773812591/4068289, 14871843858622967538884850775446891920600/8205738913)
(-4377758203129471850699/16, 106029495727655281059137213310759/64)

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