@prefix p: <http://www.wikidata.org/prop/> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix schema1: <http://schema.org/> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix wd: <http://www.wikidata.org/entity/> .
@prefix wds: <http://www.wikidata.org/entity/statement/> .
@prefix wdt: <http://www.wikidata.org/prop/direct/> .
@prefix wdtn: <http://www.wikidata.org/prop/direct-normalized/> .
@prefix wikibase: <http://wikiba.se/ontology#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

wd:Q287419 rdfs:label "J-invariant"@ca,
        "j-Funktion"@de,
        "j-invariant"@en,
        "j-invarianto"@eo,
        "j-invariante"@es,
        "j-invariantea"@eu,
        "j-invariant"@fr,
        "invariante j"@it,
        "j-不変量"@ja,
        "j-불변량"@ko,
        "j-မပြောင်းလဲသော ဂုဏ်သတ္တိ"@my,
        "j-invariant"@nl,
        "Niezmiennik j"@pl,
        "j-invariante"@pt,
        "j-invarianta"@ro,
        "J-инвариант"@ru,
        "j-invarianten"@sv,
        "j-değişmezi"@tr,
        "J-інваріант"@uk,
        "椭圆模函数"@zh,
        "j-不变量"@zh-cn,
        "J-不變量"@zh-hans,
        "j-不變數"@zh-hant ;
    schema1:dateModified "2026-10-02T13:56:29+00:00"^^xsd:dateTime ;
    schema1:description "mathematische Funktion"@de,
        "modular function of weight zero defined on the upper half-plane of complex numbers"@en,
        "fonction mathématique"@fr,
        "modulaire functie  j ( τ ) van een complexe variabele  τ"@nl ;
    schema1:version 2552181459 ;
    wikibase:identifiers 4 ;
    wikibase:sitelinks 13 ;
    wikibase:statements 13 ;
    skos:altLabel "Funció j"@ca,
        "Klein-Invariante"@de,
        "absolute Invariante"@de,
        "j-Invariante"@de,
        "j-invariant function"@en,
        "modular j-invariant"@en,
        "modula j-invarianto"@eo,
        "fonction j"@fr,
        "クラインJ-不変量"@ja,
        "楕円モジュラー函数"@ja,
        "楕円モジュラー関数"@ja,
        "母数 (楕円関数)"@ja,
        "Elliptisch modulaire functie"@nl,
        "J-niezmiennik"@pl,
        "J-不变量"@zh,
        "J-不變量"@zh,
        "J不变量"@zh,
        "J函数"@zh,
        "J变量"@zh,
        "克萊因j函數"@zh,
        "椭圓模函數"@zh,
        "椭圆模函数"@zh-cn,
        "椭圓模函數"@zh-cn,
        "J-不变量"@zh-hans,
        "J函数"@zh-hans,
        "J变量"@zh-hans,
        "椭圆模函数"@zh-hans,
        "椭圓模函數"@zh-hans,
        "J函式"@zh-hant,
        "J變數"@zh-hant,
        "J變量"@zh-hant,
        "橢圓模函式"@zh-hant ;
    p:P1568 wds:Q287419-b38f3417-4056-5187-0e42-008f0f2d1521 ;
    p:P18 wds:Q287419-75c4f4f3-4c69-cc35-c35b-fc26b7c36759,
        wds:Q287419-99994b6f-4d0b-abb2-552c-c3000c7a42d3,
        wds:Q287419-b7ec1512-4189-567b-8528-5e62a670cff4 ;
    p:P2534 wds:Q287419-7A85BAAF-92CF-4BFF-B107-7185F48CC4BE ;
    p:P2812 wds:Q287419-B815CA39-3733-47C9-AA5E-DC426C816E48 ;
    p:P31 wds:Q287419-7a5e9733-4cc7-742f-bbed-fe8a2ae3bbfe,
        wds:Q287419-91008232-4c09-ec45-5450-bbfd99130c3a ;
    p:P4215 wds:Q287419-7FEDAE30-B66B-4712-A127-33FF34511373 ;
    p:P6104 wds:Q287419-823487CC-1643-47D3-8527-ACACD9540EAD ;
    p:P6366 wds:Q287419-09B3CD4F-3160-4164-B8DF-FBE85C2880EC ;
    p:P646 wds:Q287419-1FB5EA86-92CE-4E7D-80EB-EC0CF1D18918 ;
    p:P7235 wds:Q287419-2886dbbf-4f15-04d2-2bc9-3b63d2980f5e ;
    wdtn:P6366 <https://makg.org/entity/7514240> ;
    wdt:P1568 wd:Q3258885 ;
    wdt:P18 <http://commons.wikimedia.org/wiki/Special:FilePath/J-inv-phase.jpeg>,
        <http://commons.wikimedia.org/wiki/Special:FilePath/J-inv-real.jpeg>,
        <http://commons.wikimedia.org/wiki/Special:FilePath/KleinInvariantJ.jpg> ;
    wdt:P2534 "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>j</mi><mo stretchy=\"false\">(</mo><mi>&#x03C4;</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">=</mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(</mo><mn>1</mn><mn>2</mn><munder><mo stretchy=\"false\">&#x2211;</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">&#x2260;</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\"false\">)</mo></mrow></mrow></munder><mo stretchy=\"false\">(</mo><mi>m</mi><mo stretchy=\"false\">+</mo><mi>n</mi><mi>&#x03C4;</mi><msup><mo stretchy=\"false\">)</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">&#x2212;</mo><mn>4</mn></mrow></mrow></msup><mo data-mjx-texclass=\"CLOSE\">)</mo></mrow><mrow data-mjx-texclass=\"ORD\"><mn>3</mn></mrow></msup></mrow><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(</mo><munder><mo stretchy=\"false\">&#x2211;</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">&#x2260;</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\"false\">)</mo></mrow></mrow></munder><mo stretchy=\"false\">(</mo><mi>m</mi><mo stretchy=\"false\">+</mo><mi>n</mi><mi>&#x03C4;</mi><msup><mo stretchy=\"false\">)</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">&#x2212;</mo><mn>4</mn></mrow></mrow></msup><mo data-mjx-texclass=\"CLOSE\">)</mo></mrow><mrow data-mjx-texclass=\"ORD\"><mn>3</mn></mrow></msup><mo stretchy=\"false\">&#x2212;</mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>1</mn></mrow><mrow data-mjx-texclass=\"ORD\"><mn>5</mn></mrow></mfrac></mrow><msup><mrow data-mjx-texclass=\"INNER\"><mo data-mjx-texclass=\"OPEN\">(</mo><mrow data-mjx-texclass=\"ORD\"><mfrac><mrow data-mjx-texclass=\"ORD\"><mn>7</mn></mrow><mrow data-mjx-texclass=\"ORD\"><mn>2</mn></mrow></mfrac></mrow><munder><mo stretchy=\"false\">&#x2211;</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">&#x2260;</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\"false\">)</mo></mrow></mrow></munder><mo stretchy=\"false\">(</mo><mi>m</mi><mo stretchy=\"false\">+</mo><mi>n</mi><mi>&#x03C4;</mi><msup><mo stretchy=\"false\">)</mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">&#x2212;</mo><mn>6</mn></mrow></mrow></msup><mo data-mjx-texclass=\"CLOSE\">)</mo></mrow><mrow data-mjx-texclass=\"ORD\"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> ;
    wdt:P2812 "j-Function" ;
    wdt:P31 wd:Q24034552,
        wd:Q870797 ;
    wdt:P4215 "j-invariant" ;
    wdt:P6104 wd:Q8487137 ;
    wdt:P6366 "7514240" ;
    wdt:P646 "/m/02b6jr" ;
    wdt:P7235 "<math class=\"mwe-math-element mwe-math-element-inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow data-mjx-texclass=\"ORD\"><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mi>j</mi></mstyle></mrow></math>"^^<http://www.w3.org/1998/Math/MathML> .

