Better plotting for elliptic curves

[roed314]

The plot for EllipticCurve('448c6') looks like a vertical line. The reason is that plot contains

    d = 4*x**3 + (a1**2 + 4*a2)*x**2 + (2*a3*a1 + 4*a4)*x + (a3**2 + 4*a6)
    r = d.roots(multiplicities=False)
    r.sort()
    if xmax is None:
        xmax = r[-1] + 2
    xmax = max(xmax, r[-1]+2)
    if xmin is None:
        xmin = r[0]  - 2
    xmin = min(xmin, r[0]-2)

When d has only one real root, this approach doesn't work that well. One suggestion would be to also require that the plot contains the flex points, which can be found from the 3-division polynomial.

CC: @williamstein @JohnCremona @kedlaya

Component: elliptic curves

Author: David Roe

Reviewer: Kiran Kedlaya

Merged: sage-5.0.beta14

Issue created by migration from https://trac.sagemath.org/ticket/12766

[roed314]

Attachment: 12766.patch.gz

[roed314]

Author: David Roe

[roed314]

comment:2

Ready for review. You can find a worksheet for testing at http://sagenb.org/home/pub/4639. It's all using the old code, but you can see some of the problems. Compare with the new code by downloading your own copy and running locally. This would be nicer if we had branches on sagenb already....

[roed314]

Attachment: 12766_2.patch.gz

[kedlaya]

Reviewer: Kiran Kedlaya

[kedlaya]

comment:4

Patchbot says all tests pass when applied against 5.0beta3, and looks good otherwise. Positive review.

[jdemeyer]

comment:5

I'm assuming both patches have to be applied...?

[roed314]

comment:6

Correct.

[jdemeyer]

Merged: sage-5.0.beta14