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
1183.1-a1
1183.1-a
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1183.1
\( 7 \cdot 13^{2} \)
\( 7^{2} \cdot 13^{2} \)
$1.38654$
$(-2a+1), (13)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 2 \)
$0.018270498$
$6.505570680$
0.718797813
\( \frac{110592}{91} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}+{x}$
1183.1-b1
1183.1-b
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1183.1
\( 7 \cdot 13^{2} \)
\( 7^{2} \cdot 13^{2} \)
$1.38654$
$(-2a+1), (13)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2 \)
$1.059245086$
$4.379860585$
1.558673681
\( -\frac{43614208}{91} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -7\) , \( 5\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-7{x}+5$
1183.1-b2
1183.1-b
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1183.1
\( 7 \cdot 13^{2} \)
\( 7^{18} \cdot 13^{2} \)
$1.38654$
$(-2a+1), (13)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2 \cdot 3^{2} \)
$0.117693898$
$0.486651176$
1.558673681
\( -\frac{178643795968}{524596891} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-117{x}-1245$
1183.1-b3
1183.1-b
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1183.1
\( 7 \cdot 13^{2} \)
\( 7^{6} \cdot 13^{6} \)
$1.38654$
$(-2a+1), (13)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3^{2} \)
$0.353081695$
$1.459953528$
1.558673681
\( \frac{224755712}{753571} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 13\) , \( 42\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+13{x}+42$
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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.