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Elliptic curves
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Version 10.4 Reference Manual
  • Home - Elliptic curves
  • Elliptic curve constructor
  • Construct elliptic curves as Jacobians
  • Points on elliptic curves
  • Elliptic curves over a general ring
  • Elliptic curves over a general field
  • Elliptic curves over finite fields
  • Formal groups of elliptic curves
  • Elliptic-curve morphisms
  • Composite morphisms of elliptic curves
  • Sums of morphisms of elliptic curves
  • Isomorphisms between Weierstrass models of elliptic curves
  • Isogenies
  • Square‑root Vélu algorithm for elliptic-curve isogenies
  • Scalar-multiplication morphisms of elliptic curves
  • Frobenius isogenies of elliptic curves
  • Isogenies of small prime degree
  • Modular polynomials for elliptic curves
  • Elliptic curves over the rational numbers
  • Tables of elliptic curves of given rank
  • Elliptic curves over number fields
  • Canonical heights for elliptic curves over number fields
  • Saturation of Mordell-Weil groups of elliptic curves over number fields
  • Torsion subgroups of elliptic curves over number fields (including \(\QQ\))
  • Galois representations attached to elliptic curves
  • Galois representations for elliptic curves over number fields
  • Isogeny class of elliptic curves over number fields
  • Tate-Shafarevich group
  • Complex multiplication for elliptic curves
  • Testing whether elliptic curves over number fields are \(\QQ\)-curves
  • Local data for elliptic curves over number fields
  • Kodaira symbols
  • Tate’s parametrisation of \(p\)-adic curves with multiplicative reduction
  • Weierstrass \(\wp\)-function for elliptic curves
  • Period lattices of elliptic curves and related functions
  • Regions in fundamental domains of period lattices
  • Modular parametrization of elliptic curves over \(\QQ\)
  • Modular symbols attached to elliptic curves over \(\QQ\)
  • Modular symbols by numerical integration
  • \(L\)-series for elliptic curves
  • Heegner points on elliptic curves over the rational numbers
  • \(p\)-adic \(L\)-functions of elliptic curves
  • Descent on elliptic curves over \(\QQ\) with a 2-isogeny
  • Elliptic curves with prescribed good reduction
  • Elliptic curves over padic fields
  • Denis Simon’s PARI scripts
  • Elliptic curves with congruent mod-5 representation
  • Morphism to bring a genus-one curve into Weierstrass form
  • Hyperelliptic curve constructor
  • Hyperelliptic curves over a general ring
  • Hyperelliptic curves over a finite field
  • Hyperelliptic curves over a \(p\)-adic field
  • Hyperelliptic curves over the rationals
  • Mestre’s algorithm
  • Computation of Frobenius matrix on Monsky-Washnitzer cohomology
  • Frobenius on Monsky-Washnitzer cohomology of a hyperelliptic curve
  • Jacobian of a general hyperelliptic curve
  • Jacobian of a hyperelliptic curve of genus 2
  • Rational point sets on a Jacobian
  • Jacobian ‘morphism’ as a class in the Picard group
  • Hyperelliptic curves of genus 2 over a general ring
  • Compute invariants of quintics and sextics via ‘Ueberschiebung’
  • Kummer surfaces over a general ring
  • Conductor and reduction types for genus 2 curves
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Jacobian of a hyperelliptic curve of genus 2#

class sage.schemes.hyperelliptic_curves.jacobian_g2.HyperellipticJacobian_g2(C, category=None)[source]#

Bases: HyperellipticJacobian_generic

kummer_surface()[source]#
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Rational point sets on a Jacobian
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Jacobian of a general hyperelliptic curve
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  • Jacobian of a hyperelliptic curve of genus 2
    • HyperellipticJacobian_g2
      • kummer_surface()