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I don't think it will be instructive, for learning purposes, to use a prime that big and plot it (assuming this is what you want to do) and I suspect the problem is the size of the field.

Here's the curve I use as an example, with cofactor 1, for "ecc" curves that are like NIST ones.

  E=EllipticCurve(GF(17),[3,5])
  E.order()
  E.is_supersingular()
  E.plot()

As you can see, it's a prime order group (so cofactor 1) and not supersingular, although it is obviously way too small for real world use. The plot however is nicer. Can't upload it to show you, but you can reproduce from this.