Index
INTRO | Introduction to these notes |
PRELIM | Basic theory of elliptic functions and related area's |
Y2R4 | $y^2 = ax^4 + bx^3 + cx^2 + dx + e$ |
Y3R3 | $y^3 = (ax^3 + bx^2 + cx + d)^2,\qquad y^4 = (px + q)^2(ax^2 + bx + c)^3,\qquad y^6 = (ax + b)^3(cx + d)^4(ex + f)^5$ |
X2Y2 | $a_{22} x^2 y^2 + a_{21} x^2 y + a_{20} x^2 + a_{12} x y^2 + a_{11} x y + a_{10} x + a_{02} y^2 + a_{01} y + a_{00} = 0$ |
X3Y3 | $a_{30} x^3 + a_{21} x^2 y + a_{12} x y^2 + a_{03} y^3 + a_{20} x^2 + a_{11} x y + a_{02} y^2 + a_{10} x + a_{01} y + a_{00} = 0$ |
SIGMA | Addition formulae for the Sigma and Theta Functions |
VANDERMONDE | Consequences of the Vandermonde Determinant Formula |
JAC | Jacobian Elliptic Functions |
WP Part 1 | Addition formulae for the Weierstrass $\wp$ Function |
WP Part 2 | Dual Addition formulae for the Weierstrass $\wp$ Function |
$h$ Functions | Weierstrass $h$ Functions |
ADD3 | Addition formulae for the Cubic Curve |
ADD4 | Addition formulae for the Quartic Curve |
MYSTERY | Mystery formulae |
Y2R4X | Quartic Elliptic Tour |
Y2R4X2 | Quartic Curve Intro |
Y3R3X | Scwharz-Christoffel Curve Intro |
CURVE-LIST | List Of Low Degree Genus One Curves |
LATTICE-ALIGNED | Lattice Aligned Order 2 Elliptic Functions |
SYMADD | Five Symmetric Addition formulae |
ADD34 | Summary of addition formulae for Cubic and Quartic Curves |
CLASVSYM | Classic vs Symmetric Addition Formulae |
UNEXPECTED | Unexpected Symmetry |
CIRC | Addition formulae for the Circle |
ABEL | Abel's addition formulae overview |
MODULARITY | Modularity Theorem |
FXY | $F(x,y)=0$ |
FXY2 | $F(x,y)=0$ |
MISC | Miscellaneous stuff |
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