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
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{8} \)
$0.61910$
$(2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$2$
2Cs
$1$
\( 1 \)
$1$
$8.847515954$
0.638514464
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}$
256.1-CMb2
256.1-CMb
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$0.61910$
$(2)$
0
$\Z/4\Z$
$\textsf{yes}$
$-12$
$\mathrm{U}(1)$
✓
✓
$1$
\( 2 \)
$1$
$4.423757977$
0.638514464
\( 54000 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a\) , \( 8 a - 4\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-4a{x}+8a-4$
256.1-CMa1
256.1-CMa
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{8} \)
$0.61910$
$(2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$2$
2Cs
$1$
\( 1 \)
$1$
$8.847515954$
0.638514464
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}$
256.1-CMa2
256.1-CMa
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$0.61910$
$(2)$
0
$\Z/4\Z$
$\textsf{yes}$
$-12$
$\mathrm{U}(1)$
✓
✓
$1$
\( 2 \)
$1$
$4.423757977$
0.638514464
\( 54000 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 5\) , \( -3 a - 1\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-5\right){x}-3a-1$
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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.