I want to use a SageMath constructor for Elliptic Curves that receives a polinomial `EllipticCurve(polynomial)`. Until now I'm using in my experiments the constructor with j-invariant `EllipticCurve(j=j0)`. However, I did some comparison and found that using the j-invariant constructor is faster than the polinomial constructor, if after construct the curve, I check for `is_supersingular` property. Why this happen? Have the constructors the same computational complexity? Or the advantage lives in the `is_supersingular` calculation ?
Yes, SageMath has an Elliptic Curve constructor that takes a polynomial as an argument and is faster than the one that takes the j-invariant. The constructor is called the MordellWeilGroup constructor and it is available in the sage.schemes.elliptic_curves.constructor module.
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