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
5184.4-a1
5184.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5184.4
\( 2^{6} \cdot 3^{4} \)
\( 2^{22} \cdot 3^{28} \)
$2.00611$
$(a), (-a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$6.551017245$
$0.302945584$
3.000435819
\( \frac{207646}{6561} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 141\) , \( 4718\bigr] \)
${y}^2={x}^{3}+141{x}+4718$
5184.4-a2
5184.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5184.4
\( 2^{6} \cdot 3^{4} \)
\( 2^{8} \cdot 3^{14} \)
$2.00611$
$(a), (-a+1), (3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.818877155$
$2.423564678$
3.000435819
\( \frac{2048}{3} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -7\bigr] \)
${y}^2={x}^{3}+6{x}-7$
5184.4-a3
5184.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5184.4
\( 2^{6} \cdot 3^{4} \)
\( 2^{16} \cdot 3^{16} \)
$2.00611$
$(a), (-a+1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1.637754311$
$1.211782339$
3.000435819
\( \frac{35152}{9} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -39\) , \( -70\bigr] \)
${y}^2={x}^{3}-39{x}-70$
5184.4-a4
5184.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5184.4
\( 2^{6} \cdot 3^{4} \)
\( 2^{20} \cdot 3^{20} \)
$2.00611$
$(a), (-a+1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$3.275508622$
$0.605891169$
3.000435819
\( \frac{1556068}{81} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -219\) , \( 1190\bigr] \)
${y}^2={x}^{3}-219{x}+1190$
5184.4-a5
5184.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5184.4
\( 2^{6} \cdot 3^{4} \)
\( 2^{20} \cdot 3^{14} \)
$2.00611$
$(a), (-a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.818877155$
$0.605891169$
3.000435819
\( \frac{28756228}{3} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -579\) , \( -5362\bigr] \)
${y}^2={x}^{3}-579{x}-5362$
5184.4-a6
5184.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
5184.4
\( 2^{6} \cdot 3^{4} \)
\( 2^{22} \cdot 3^{16} \)
$2.00611$
$(a), (-a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$6.551017245$
$0.302945584$
3.000435819
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3459\) , \( 78302\bigr] \)
${y}^2={x}^{3}-3459{x}+78302$
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Pari/GP
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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.