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I have no problems to investigate some points on the curve. For instance:

E10 = EllipticCurve( GF(p1), [-3,0] )
P,  = E10.gens()
E10.gens() == [ P, ]    # True

print P.order().factor()
# 2^2 * 17 * 31 * 43 * 23081 * 4552451 * 188515208046969049479851413 * 64490171990641492934559272183431339

k = P.order() / 17
k = ZZ(k)
Q = k * P
x, y, _ = Q
print "k = %s" % k
print "Q = k*P"
print "Q has the following coordinates x, y:"
print "x = %s" % x
print "y = %s" % y


After a %cpaste into the interpreter:

True
2^2 * 17 * 31 * 43 * 23081 * 4552451 * 188515208046969049479851413 * 64490171990641492934559272183431339
k = 6811299366900952671974763824040465167839410862684739061144563765171360567044
Q = k*P
Q has the following coordinates x, y:
x = 27437129805757554196750179718248270297390475505636928792989955318129458214854
y = 72861835628999598253805209504126577415537834053407849625158220308472740134763


More cannot be reproduced. We need the print commands and the points to be printed.