@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-V27F12ZJ-1
  skos:prefLabel "elliptic integral"@en, "intégrale elliptique"@fr ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr: a skos:ConceptScheme .
psr:-TR47562N-J
  skos:prefLabel "Mordell-Weil group"@en, "groupe de Mordell-Weil"@fr ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-GS4TJ5TT-Z
  skos:prefLabel "conjecture de Birch et Swinnerton-Dyer"@fr, "Birch and Swinnerton-Dyer conjecture"@en ;
  a skos:Concept ;
  skos:related psr:-JXHC9RBH-S .

psr:-MJS17JXT-S
  skos:prefLabel "Schoof's algorithm"@en, "algorithme de Schoof"@fr ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-ZXC84VMK-T
  skos:prefLabel "Hasse's theorem on elliptic curves"@en, "théorème de Hasse sur les courbes elliptiques"@fr ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-QP0D47D3-D
  skos:prefLabel "courbe algébrique"@fr, "algebraic curve"@en ;
  a skos:Concept ;
  skos:narrower psr:-JXHC9RBH-S .

psr:-NZ2SQG72-M
  skos:prefLabel "Schottky problem"@en, "problème de Schottky"@fr ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-NC1L3FGR-D
  skos:prefLabel "conjecture de torsion"@fr, "torsion conjecture"@en ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-KSC7THDV-3
  skos:prefLabel "semistable abelian variety"@en, "variété abélienne semi-stable"@fr ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-KX320X68-4
  skos:prefLabel "équation de Picard-Fuchs"@fr, "Picard-Fuchs equation"@en ;
  a skos:Concept ;
  skos:related psr:-JXHC9RBH-S .

psr:-JXHC9RBH-S
  skos:narrower psr:-ZXC84VMK-T, psr:-NC1L3FGR-D, psr:-X7PWRX50-P, psr:-PMS4JGGS-1, psr:-RJGTKL0W-6, psr:-FDMMJ0JC-0, psr:-TR47562N-J, psr:-MJS17JXT-S, psr:-KSC7THDV-3, psr:-NZ2SQG72-M, psr:-V27F12ZJ-1, psr:-NQTXBMJS-Z ;
  skos:broader psr:-QP0D47D3-D, psr:-F7SFNL4R-1 ;
  skos:inScheme psr: ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Courbe_elliptique>, <https://en.wikipedia.org/wiki/Elliptic_curve> ;
  skos:related psr:-GS4TJ5TT-Z, psr:-KX320X68-4 ;
  dc:modified "2023-08-17"^^xsd:date ;
  skos:prefLabel "elliptic curve"@en, "courbe elliptique"@fr ;
  a skos:Concept ;
  skos:definition """In mathematics, an <b>elliptic curve</b> is a smooth, projective, algebraic curve of genus one, on which there is a specified point <span class="texhtml mvar" style="font-style:italic;">O</span>. An elliptic curve is defined over a field <span class="texhtml mvar" style="font-style:italic;">K</span> and describes points in <span class="texhtml"><i>K</i><span style="padding-left:0.12em;"><sup>2</sup></span></span>, the Cartesian product of <span class="texhtml mvar" style="font-style:italic;">K</span> with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions <span class="texhtml">(<i>x</i>, <i>y</i>)</span> for:
<br/>
<br/><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle y^{2}=x^{3}+ax+b}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>y</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>=</mo>
<br/>        <msup>
<br/>          <mi>x</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>3</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mo>+</mo>
<br/>        <mi>a</mi>
<br/>        <mi>x</mi>
<br/>        <mo>+</mo>
<br/>        <mi>b</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle y^{2}=x^{3}+ax+b}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3dbe6cab1bc2c7f1c99757dc6e5d7a517cf9b4f8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:16.935ex; height:3.009ex;" alt="y^{2}=x^{3}+ax+b"></span></dd></dl>
<br/>for some coefficients <span class="texhtml mvar" style="font-style:italic;">a</span> and <span class="texhtml mvar" style="font-style:italic;">b</span> in <span class="texhtml mvar" style="font-style:italic;">K</span>. The curve is required to be non-singular, which means that the curve has no cusps or self-intersections. (This is equivalent to the condition <span class="texhtml">4<i>a</i><sup>3</sup> + 27<i>b</i><sup>2</sup> ≠ 0</span>, that is, being square-free in <span class="texhtml mvar" style="font-style:italic;">x</span>.)  It is always understood that the curve is really sitting in the projective plane, with the point <span class="texhtml mvar" style="font-style:italic;">O</span> being the unique point at infinity. Many sources define an elliptic curve to be simply a curve given by an equation of this form. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Elliptic_curve">https://en.wikipedia.org/wiki/Elliptic_curve</a>)"""@en, """En mathématiques, une courbe elliptique est un cas particulier de courbe algébrique, munie entre autres propriétés d'une addition géométrique sur ses points. Les courbes elliptiques ont de nombreuses applications dans des domaines très différents des mathématiques : elles interviennent ainsi en mécanique classique dans la description du mouvement des toupies, en théorie des nombres dans la démonstration du dernier théorème de Fermat, en cryptologie dans le problème de la factorisation des entiers ou pour fabriquer des codes performants. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Courbe_elliptique">https://fr.wikipedia.org/wiki/Courbe_elliptique</a>)"""@fr .

psr:-F7SFNL4R-1
  skos:prefLabel "algebraic number theory"@en, "théorie algébrique des nombres"@fr ;
  a skos:Concept ;
  skos:narrower psr:-JXHC9RBH-S .

psr:-NQTXBMJS-Z
  skos:prefLabel "fonction de hauteur"@fr, "height function"@en ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-RJGTKL0W-6
  skos:prefLabel "courbe elliptique supersingulière"@fr, "supersingular elliptic curve"@en ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-FDMMJ0JC-0
  skos:prefLabel "Sato-Tate conjecture"@en, "conjecture de Satō-Tate"@fr ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-PMS4JGGS-1
  skos:prefLabel "complex multiplication"@en, "multiplication complexe"@fr ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .

psr:-X7PWRX50-P
  skos:prefLabel "Mordell-Weil theorem"@en, "théorème de Mordell-Weil"@fr ;
  a skos:Concept ;
  skos:broader psr:-JXHC9RBH-S .