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
392.1-b1
392.1-b
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{2} \)
$1.12462$
$(a), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$6.395739286$
2.261235310
\( -\frac{4}{7} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 1\) , \( 1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+{x}+1$
784.1-a1
784.1-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{2} \)
$1.33740$
$(a), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$0.239919898$
$6.395739286$
1.085030693
\( -\frac{4}{7} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}$
19208.1-b1
19208.1-b
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
19208.1
\( 2^{3} \cdot 7^{4} \)
\( 2^{8} \cdot 7^{14} \)
$2.97546$
$(a), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.844493815$
$0.913677040$
2.182399124
\( -\frac{4}{7} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( -174\bigr] \)
${y}^2+a{x}{y}={x}^{3}-4{x}-174$
31752.3-f1
31752.3-f
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
31752.3
\( 2^{3} \cdot 3^{4} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{12} \cdot 7^{2} \)
$3.37385$
$(a), (-a-1), (a-1), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.436951865$
$2.131913095$
5.269605267
\( -\frac{4}{7} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( 1\) , \( -13\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+{x}-13$
38416.1-i1
38416.1-i
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
38416.1
\( 2^{4} \cdot 7^{4} \)
\( 2^{8} \cdot 7^{14} \)
$3.53844$
$(a), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{3} \)
$1$
$0.913677040$
5.168537851
\( -\frac{4}{7} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -4\) , \( 174\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-4{x}+174$
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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.