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The set is [(0, 1, 0), (0, 3), (0, 4), (1, 0), (2, 2), (2, 5), (5, 0), (6, 2), (6, 5)]
The identity of this set is (0, 1, 0)
The set is closed under addition.
Every element in this set has an inverse.
The set is not associative under addition.
((0, 3) + (1, 0)) + (1, 0) = (0, 1, 0) != (0, 3) = (0, 3) + ((1, 0) + (1, 0))
Elliptic Curve defined by y^2 = x^3 + x - 11 over Rational Field
x |--> x^3 - 729/64*x^2 + 1323/32*x - 3105/64
(345/64, 6179/512)
(3, 4)
Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 7
The elements of Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 7
are [(0, 0), (0, 1, 0), (1, 3), (1, 4), (3, 3), (3, 4), (5, 2), (5, 5)]
The identity of this set is (0, 1, 0)
The set is closed under addition.
Every element in this set has an inverse.
This set is associative under addition.
This set is cyclic and generated by (3, 3)
[(0, 1, 0), (3, 3), (1, 4), (5, 5), (0, 0), (5, 2), (1, 3), (3, 4), (0, 1, 0)]
This set is cyclic and generated by (3, 4)
[(0, 1, 0), (3, 4), (1, 3), (5, 2), (0, 0), (5, 5), (1, 4), (3, 3), (0, 1, 0)]
This set is cyclic and generated by (5, 2)
[(0, 1, 0), (5, 2), (1, 4), (3, 4), (0, 0), (3, 3), (1, 3), (5, 5), (0, 1, 0)]
This set is cyclic and generated by (5, 5)
[(0, 1, 0), (5, 5), (1, 3), (3, 3), (0, 0), (3, 4), (1, 4), (5, 2), (0, 1, 0)]