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- from sympy.ntheory.elliptic_curve import EllipticCurve
- def test_elliptic_curve():
- # Point addition and multiplication
- e3 = EllipticCurve(-1, 9)
- p = e3(0, 3)
- q = e3(-1, 3)
- r = p + q
- assert r.x == 1 and r.y == -3
- r = 2*p + q
- assert r.x == 35 and r.y == 207
- r = -p + q
- assert r.x == 37 and r.y == 225
- # Verify result in http://www.lmfdb.org/EllipticCurve/Q
- # Discriminant
- assert EllipticCurve(-1, 9).discriminant == -34928
- assert EllipticCurve(-2731, -55146, 1, 0, 1).discriminant == 25088
- # Torsion points
- assert len(EllipticCurve(0, 1).torsion_points()) == 6
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