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In the above section we graphed as a function of . In reality however, both and
are defined on as well. Using a mixture of PARI and Mathematica we were able to produce graphs of
and
for various elliptic curves.
Figure 8 is a graph of the argument of
for the elliptic curve
.
Figure 8:
The argument of for
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We can also see the absolute value of
for
in Figure 9.
Figure 9:
The absolute value of for
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Ariel Shwayder
2002-12-11
![\includegraphics{graph[0,-1,1,-10,-20].abs.eps}](img102.png)