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Elliptic Curve

Named curves

Burnside curve | Mordell elliptic curve | Ochoa elliptic curve | semicubical parabola

Example plots

Example plots Burnside curve

Example plots Mordell elliptic curve

Example plots Ochoa elliptic curve

Example plots Semicubical parabola

Alternate names

cuspidal cubic curve | Neile parabola

Equations

semicubical parabola | x(t) = a t^2
y(t) = a t^3

Burnside curve | y^2 = x (x^4 - 1)
Mordell elliptic curve | y^2 = n + x^3
Ochoa elliptic curve | y^2 = x^3 - 440067 x + 106074110
semicubical parabola | y^2 = a^2 x^3

semicubical parabola | r(θ) = a tan^2(θ) sec(θ)

Common properties

algebraic | elliptic

Basic properties

Burnside curve | A = (sqrt(π) Γ(3/8))/(4 Γ(15/8))

Burnside curve | d = 5
Mordell elliptic curve | d = 3
Ochoa elliptic curve | d = 3
semicubical parabola | d = 3

Derived curves

| involute
semicubical parabola | parabola

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