## Elliptic Curves Assignment Help

Elliptic curves are algebraic curves which trace their trajectory by one or more than one points of interest, known as focus and are defined by their eccentricity. These curves can be classified into parabola, hyperbolae and ellipses.The equation that defines the elliptic curve (EC) is : y2 = x3 + ax + b. The elliptic curves changes based on the values of a and b.

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The Modularity Theorem | Algebraic Curves |

Riemann-Roch Theorem | Weierstrass Form |

Minimal Weierstrass Equation | Elliptic Curves over a General Field |

Elliptic Curves over the Real Numbers | Tate Module |

Hasse Invariant | Mordell-Weil Theorem |

Elliptic Curves over Local Fields | Kummer Pairing |

Elliptic Curve DSA | Twisted Edwards Curve |

Hessian Curve | Edwards Curve |

Neron-Ogg-Shafarevich criterion for Good Reduction | Elliptic Curves over Global Fields |

Weil Conjectures | Twisted Hessian Curve |

Elliptic Curves over the Complex Numbers | Uniformization |

Twisted Curve | Elliptic Curves over Finite Fields |

The Group Law | Isogeny |

Elliptic Curve Cryptography | Doubling-Oriented Doche–Icart–Kohel Curve |

Nagell-Lutz Theorem | Tripling-Oriented Doche–Icart–Kohel Curve |

Jacobian Curve | Elliptic Curve Diffie–Hellman |