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
256.4-a1
256.4-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
256.4
\( 2^{8} \)
\( 2^{19} \)
$0.94569$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$3.081235671$
1.164597616
\( -237572 a - 285952 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a + 10\) , \( 8 a - 20\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+10\right){x}+8a-20$
256.4-a2
256.4-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
256.4
\( 2^{8} \)
\( 2^{22} \)
$0.94569$
$(a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.081235671$
1.164597616
\( 3084 a - 65800 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a - 5\) , \( -11 a + 5\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-5\right){x}-11a+5$
256.4-a3
256.4-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
256.4
\( 2^{8} \)
\( 2^{14} \)
$0.94569$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$6.162471343$
1.164597616
\( 336 a + 224 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-a{x}$
256.4-a4
256.4-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
256.4
\( 2^{8} \)
\( 2^{13} \)
$0.94569$
$(a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$6.162471343$
1.164597616
\( -2056 a + 4824 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+{x}$
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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.