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Gregg Kelly

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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