These lines in the doctest is incorrect:

The elliptic curve actually has order 12, as shown by printing E.points():

sage: E.points()
[(0 : 1 : 0), (0 : 1 : 1), (0 : 6 : 1), (1 : 3 : 1), (1 : 4 : 1), (2 : 3 : 1), (2 : 4 : 1), (3 : 0 : 1), (4 : 3 : 1), (4 : 4 : 1), (5 : 0 : 1), (6 : 0 : 1)]

Additional Information

All points have order $6$, but not all groups are abelian!

Fixed in #37119.