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@@ -0,0 +1,25 @@
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+q = 67
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+K.<x> = GF(q)[]
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+F1.<u> = K.extension(x^2 + 1)
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+F2.<v> = F1.extension(x^3 + 2)
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+
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+E = EllipticCurve(F2, [4, 3])
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+
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+print(E)
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+pi_i = F2.frobenius_endomorphism()
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+#print(pi)
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+
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+def pi(p):
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+ return E(pi_i(p[0]), pi_i(p[1]))
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+
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+P1 = E(15, 50)
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+print(pi(P1))
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+
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+P2 = E(2*u + 16, 30*u + 39)
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+print(pi(P2))
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+
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+P3 = E(15*v^2 + 4*v + 8, 44*v^2 + 30*v + 21)
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+print(pi(P3))
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+print(pi(pi(P3)))
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+print(pi(pi(pi(P3))))
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+
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narodnik