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
128.4-a1
128.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
128.4
\( 2^{7} \)
\( 2^{21} \)
$0.79523$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5S4
$1$
\( 2 \)
$1$
$2.400503441$
0.907305018
\( -1097726 a - 998656 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a - 22\) , \( -40 a + 16\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(21a-22\right){x}-40a+16$
128.4-a2
128.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
128.4
\( 2^{7} \)
\( 2^{21} \)
$0.79523$
$(a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5S4
$1$
\( 2^{3} \)
$1$
$2.400503441$
0.907305018
\( 1097726 a - 2096382 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a - 1\) , \( -40 a + 24\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-21a-1\right){x}-40a+24$
128.4-a3
128.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
128.4
\( 2^{7} \)
\( 2^{15} \)
$0.79523$
$(a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5S4
$1$
\( 2^{2} \)
$1$
$4.801006883$
0.907305018
\( -28658 a + 8966 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 4\) , \( a - 2\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-4\right){x}+a-2$
128.4-a4
128.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
128.4
\( 2^{7} \)
\( 2^{15} \)
$0.79523$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2B , 5S4
$1$
\( 1 \)
$1$
$4.801006883$
0.907305018
\( 28658 a - 19692 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 2\) , \( a + 1\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-2a-2\right){x}+a+1$
128.4-a5
128.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
128.4
\( 2^{7} \)
\( 2^{18} \)
$0.79523$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2Cs , 5S4
$1$
\( 2^{2} \)
$1$
$4.801006883$
0.907305018
\( -924 a + 1784 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 2\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-2\right){x}$
128.4-a6
128.4-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
128.4
\( 2^{7} \)
\( 2^{18} \)
$0.79523$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 5$
2Cs , 5S4
$1$
\( 2^{4} \)
$1$
$4.801006883$
0.907305018
\( 924 a + 860 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-a-1\right){x}$
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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.