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
9.1-a1
9.1-a
$4$
$10$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( 3^{20} \)
$0.43777$
$(3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.1.2
$1$
\( 2 \)
$1$
$1.266923342$
0.223962521
\( -\frac{873722816}{59049} \)
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -40 a - 60\) , \( -153 a - 220\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-40a-60\right){x}-153a-220$
9.1-a2
9.1-a
$4$
$10$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( 3^{4} \)
$0.43777$
$(3)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \)
$1$
$31.67308356$
0.223962521
\( \frac{64}{9} \)
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}$
9.1-a3
9.1-a
$4$
$10$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( 3^{2} \)
$0.43777$
$(3)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.1.1
$1$
\( 1 \)
$1$
$63.34616712$
0.223962521
\( \frac{85184}{3} \)
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -2 a - 3\) , \( 0\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2a-3\right){x}$
9.1-a4
9.1-a
$4$
$10$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
9.1
\( 3^{2} \)
\( 3^{10} \)
$0.43777$
$(3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5B.1.2
$1$
\( 1 \)
$1$
$2.533846685$
0.223962521
\( \frac{58591911104}{243} \)
\( \bigl[a\) , \( a\) , \( a + 1\) , \( -162 a - 243\) , \( -1495 a - 2130\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-162a-243\right){x}-1495a-2130$
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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.