Elliptic Curves and Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg40808] Elliptic Curves and Mathematica
- From: "flip" <flip_alpha at safebunch.com>
- Date: Sat, 19 Apr 2003 22:59:19 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello,
I am working on Elliptic Curves and was wondering if these are doable in
Mathematica? I can do them manually, but was wondering if it is possible to show in
Mathematica).
a. The following point has finite order on the given elliptic curve over Q.
Find the order of P.
P = (0, 16) on y^2 = x^3 + 256 (Answer is 3)
b. Is it possible to plot the elliptic curve y^2 = x^3 - x in the xy-plane?
(I'd like to be able to plot the elliptic curve and then superimpose lines
through it and verify things like Bezout's Theorem, where possible of course
as L{infinity} is not viewable.)
c. Is it possible to show that y^2 = x^3 - 36 x and let P = (-3, 9) and Q =
(-2, 8).
i.) Is it possible to find P + Q (Answer is (6, 0))
ii.) Is it possible to find 2P (Answer is (25/4, -35/8))
I am trying to get to the point where I have a few function to help me with
elliptic curve cryptography.
Thanks for any insights (note, these may be quite easy in Mathematica and I haven't
really given it much thought, if so please forgive my posting).
Thanks,
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