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
256.1-CMb1
256.1-CMb
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{12} \)
$1.01098$
$(a)$
0
$\Z/2\Z$
$\textsf{yes}$
$-8$
$\mathrm{U}(1)$
✓
✓
$1$
\( 1 \)
$1$
$6.344993467$
1.121646976
\( 8000 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( a\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+{x}+a$
256.1-CMa1
256.1-CMa
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{12} \)
$1.01098$
$(a)$
0
$\Z/2\Z$
$\textsf{yes}$
$-8$
$\mathrm{U}(1)$
✓
✓
$1$
\( 1 \)
$1$
$6.344993467$
1.121646976
\( 8000 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -a\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+{x}-a$
256.1-a1
256.1-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$1.01098$
$(a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.108082791$
$5.544794010$
0.847533680
\( 128 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 1\bigr] \)
${y}^2={x}^{3}+{x}^{2}+{x}+1$
256.1-a2
256.1-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{14} \)
$1.01098$
$(a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$0.216165582$
$5.544794010$
0.847533680
\( 10976 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \)
${y}^2={x}^{3}+{x}^{2}-2{x}-2$
256.1-b1
256.1-b
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$1.01098$
$(a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$5.544794010$
1.960380722
\( 128 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( -1\bigr] \)
${y}^2={x}^{3}-{x}^{2}+{x}-1$
256.1-b2
256.1-b
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{14} \)
$1.01098$
$(a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$5.544794010$
1.960380722
\( 10976 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \)
${y}^2={x}^{3}-{x}^{2}-2{x}+2$
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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.