# Arithmetic Geometry

Rational Curves and ConicsRational curves and conics: models and rational points.

[Rational Curves and Conics](RationalCurvesAndConics/index-rational-curves-and-conics.md)Elliptic CurvesElliptic curve creation, arithmetic and the function field.

[Elliptic Curves](EllipticCurves/index-elliptic-curves.md)Elliptic Curves over Finite FieldsSupersingular curves, point counting, group structure and pairings.

[Elliptic Curves over Finite Fields](EllipticCurvesOverFiniteFields/index-elliptic-curves-over-finite-fields.md)Elliptic Curves over Q and Number FieldsCurves over number fields and p-adic fields, and Mordell-Weil groups.

[Elliptic Curves over {\mathbb{Q}} and Number Fields](EllipticCurvesOverQAndNumberFields/index-elliptic-curves-over-qand-number-fields.md)Elliptic Curves over Function FieldsCurve search, heights and torsion over function fields.

[Elliptic Curves over Function Fields](EllipticCurvesOverFunctionFields/index-elliptic-curves-over-function-fields.md)Models of Genus One CurvesGenus one curve models, transformations and equivalence.

[Models of Genus One Curves](ModelsOfGenusOneCurves/index-models-of-genus-one-curves.md)Plane QuarticsQuartic invariants, reconstruction from invariants, and twists.

[Plane Quartics](PlaneQuartics/index-plane-quartics.md)Hyperelliptic CurvesHyperelliptic curve models and divisor arithmetic.

[Hyperelliptic Curves](HyperellipticCurves/index-hyperelliptic-curves.md)Hypergeometric MotivesHypergeometric motives and Jacobi motives.

[Hypergeometric Motives](HypergeometricMotives/index-hypergeometric-motives.md)L-FunctionsBuilt-in and general L-series, and their invariants.

[L-Functions](LFunctions/index-lfunctions.md)