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
15842.2-a1
15842.2-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
15842.2
\( 2 \cdot 89^{2} \)
\( 2^{28} \cdot 89^{2} \)
$2.83554$
$(a), (-2a+9), (2a+9)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$7.429595304$
$1.204226331$
6.326423772
\( \frac{9759185353}{1458176} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -44\) , \( 80\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-44{x}+80$
15842.2-a2
15842.2-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
15842.2
\( 2 \cdot 89^{2} \)
\( 2^{14} \cdot 89^{4} \)
$2.83554$
$(a), (-2a+9), (2a+9)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$3.714797652$
$0.602113165$
6.326423772
\( \frac{35471840526793}{1013888} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -684\) , \( 6608\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}-684{x}+6608$
15842.2-b1
15842.2-b
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
15842.2
\( 2 \cdot 89^{2} \)
\( 2^{8} \cdot 89^{6} \)
$2.83554$
$(a), (-2a+9), (2a+9)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2^{3} \)
$1$
$0.551982120$
3.122482403
\( -\frac{18806241149857}{11279504} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -554\) , \( -5068\bigr] \)
${y}^2+{x}{y}={x}^{3}-554{x}-5068$
15842.2-b2
15842.2-b
$2$
$3$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
15842.2
\( 2 \cdot 89^{2} \)
\( 2^{24} \cdot 89^{2} \)
$2.83554$
$(a), (-2a+9), (2a+9)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2^{3} \cdot 3 \)
$1$
$1.655946361$
3.122482403
\( \frac{23639903}{364544} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( 6\) , \( -28\bigr] \)
${y}^2+{x}{y}={x}^{3}+6{x}-28$
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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.