Hej Niles,
I wonder why in your example you do the quadratic twist thing. In this
case E is equal to it's quadratic twist. (at least without the patch).
sage: E = EllipticCurve('53a1')
sage: Et, D = E.minimal_quadratic_twist()
sage: E
Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 over Rational
Field
sage: Et
Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 over Rational
Field
sage: D
1
Have you already tried to use the equation in the docstring of
Dp_valued_series which it's output has to satisfy to determine the
right awnser?
Kind Regards,
Maarten Derickx
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