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
441.2-a2
441.2-a
$6$
$8$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
441.2
\( 3^{2} \cdot 7^{2} \)
\( 3^{4} \cdot 7^{2} \)
$1.15823$
$(-a-1), (a-1), (7)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$6.896615437$
1.219160885
\( \frac{103823}{63} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}$
3969.3-c2
3969.3-c
$6$
$8$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
3969.3
\( 3^{4} \cdot 7^{2} \)
\( 3^{16} \cdot 7^{2} \)
$2.00611$
$(-a-1), (a-1), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.298871812$
1.625547847
\( \frac{103823}{63} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}$
7056.2-a2
7056.2-a
$6$
$8$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
7056.2
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{12} \cdot 3^{4} \cdot 7^{2} \)
$2.31645$
$(a), (-a-1), (a-1), (7)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.091000020$
$3.448307718$
3.550197289
\( \frac{103823}{63} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 4\) , \( 0\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+4{x}$
21609.2-a2
21609.2-a
$6$
$8$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
21609.2
\( 3^{2} \cdot 7^{4} \)
\( 3^{4} \cdot 7^{14} \)
$3.06438$
$(-a-1), (a-1), (7)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1.717899296$
$0.985230776$
2.393595003
\( \frac{103823}{63} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 48\) , \( 48\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+48{x}+48$
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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.