Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
576.1-a1
576.1-a
$6$
$8$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{16} \)
$5.58905$
$(2), (3)$
$0 \le r \le 1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
\( 2^{3} \)
$1$
$0.908836754$
6.661758943
\( \frac{207646}{6561} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \)
${y}^2={x}^3-{x}^2+16{x}-180$
576.1-a2
576.1-a
$6$
$8$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$5.58905$
$(2), (3)$
$0 \le r \le 1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
\( 2 \)
$1$
$7.270694035$
6.661758943
\( \frac{2048}{3} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2={x}^3-{x}^2+{x}$
576.1-a3
576.1-a
$6$
$8$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{4} \)
$5.58905$
$(2), (3)$
$0 \le r \le 1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
\( 2^{3} \)
$1$
$3.635347017$
6.661758943
\( \frac{35152}{9} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \)
${y}^2={x}^3-{x}^2-4{x}+4$
576.1-a4
576.1-a
$6$
$8$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{8} \)
$5.58905$
$(2), (3)$
$0 \le r \le 1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
\( 2^{3} \)
$1$
$1.817673508$
6.661758943
\( \frac{1556068}{81} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \)
${y}^2={x}^3-{x}^2-24{x}-36$
576.1-a5
576.1-a
$6$
$8$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{2} \)
$5.58905$
$(2), (3)$
$0 \le r \le 1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
\( 2 \)
$1$
$1.817673508$
6.661758943
\( \frac{28756228}{3} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \)
${y}^2={x}^3-{x}^2-64{x}+220$
576.1-a6
576.1-a
$6$
$8$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{4} \)
$5.58905$
$(2), (3)$
$0 \le r \le 1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
\( 2 \)
$1$
$0.908836754$
6.661758943
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \)
${y}^2={x}^3-{x}^2-384{x}-2772$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.