Challenge: exclude rational points of order forty-nine #
The recommended route is to bridge the marked seven-isogeny tower to the
already compiled rational-point classification of the explicit X_0(49)
correspondence.
theorem
MazurTheorem.Challenge.no_rational_point_of_order_fortyNine
(E : WeierstrassCurve ℚ)
[E.IsElliptic]
(P : (WeierstrassCurve.Affine.baseChange E ℚ).Point)
:
An elliptic curve over the rationals has no rational point of exact additive order forty-nine.