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-b2
392.1-b
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{10} \cdot 7^{4} \)
$1.12462$
$(a), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$3.197869643$
2.261235310
\( \frac{3543122}{49} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -9\) , \( 11\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-9{x}+11$
784.1-a2
784.1-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{10} \cdot 7^{4} \)
$1.33740$
$(a), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.119959949$
$3.197869643$
1.085030693
\( \frac{3543122}{49} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -9\) , \( -10\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-9{x}-10$
19208.1-b2
19208.1-b
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
19208.1
\( 2^{3} \cdot 7^{4} \)
\( 2^{10} \cdot 7^{16} \)
$2.97546$
$(a), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1.688987630$
$0.456838520$
2.182399124
\( \frac{3543122}{49} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -494\) , \( -4094\bigr] \)
${y}^2+a{x}{y}={x}^{3}-494{x}-4094$
31752.3-f2
31752.3-f
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
31752.3
\( 2^{3} \cdot 3^{4} \cdot 7^{2} \)
\( 2^{10} \cdot 3^{12} \cdot 7^{4} \)
$3.37385$
$(a), (-a-1), (a-1), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.873903731$
$1.065956547$
5.269605267
\( \frac{3543122}{49} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -89\) , \( -283\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-89{x}-283$
38416.1-i2
38416.1-i
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
38416.1
\( 2^{4} \cdot 7^{4} \)
\( 2^{10} \cdot 7^{16} \)
$3.53844$
$(a), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{4} \)
$1$
$0.456838520$
5.168537851
\( \frac{3543122}{49} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -494\) , \( 4094\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-494{x}+4094$
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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.