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\centerline{\hskip -0.5in{\bf The rank 5 curve of smallest conductor}}
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$$
y^2+y=x^3-79x+342, \qquad \Delta = -19047851
$$
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$$
c_4=3792\quad c_6=-295704
$$
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$$
\Omega = 2.04764\dots
$$
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\hskip 0.5in $L^{(1)}(E,1)$ and $L^{(3)}(E,1)$ are zero to several places, and
$$
{L^{(5)}(E,1)\over 5!}\approx 30.285711\dots, \qquad {\rm (using\ 4000\ terms)}
$$
\hskip 0.5in A basis for $E({\bf Q})$ is given by points with $x=5$, 4, 3, 7, 0,
and $$
R=14.790528\dots
$$
\hskip 0.5in And note that 
$$
{L^{(5)}(E,1)\over 5!\Omega}\approx 14.790539\dots 
$$
\bye