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
4.3-a1
4.3-a
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
4.3
\( 2^{2} \)
\( 2^{4} \)
$2.00136$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$98.10329547$
1.379685384
\( 342336 a^{2} + 460416 a - 292544 \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 3\) , \( a + 1\) , \( -2770 a^{2} + 1478 a + 11792\) , \( 1679357 a^{2} - 888891 a - 7135787\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-2770a^{2}+1478a+11792\right){x}+1679357a^{2}-888891a-7135787$
16.5-a2
16.5-a
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
16.5
\( 2^{4} \)
\( 2^{4} \)
$2.52156$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$152.8488957$
2.149605541
\( 342336 a^{2} + 460416 a - 292544 \)
\( \bigl[a^{2} + a - 2\) , \( -a + 1\) , \( a + 1\) , \( -2775 a^{2} + 1470 a + 11796\) , \( -1678490 a^{2} + 888455 a + 7132145\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2775a^{2}+1470a+11796\right){x}-1678490a^{2}+888455a+7132145$
64.1-c1
64.1-c
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
64.1
\( 2^{6} \)
\( 2^{16} \)
$3.17696$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 3 \)
$1$
$32.45491701$
1.369298792
\( 342336 a^{2} + 460416 a - 292544 \)
\( \bigl[0\) , \( a^{2} + a - 3\) , \( 0\) , \( -a^{2} + 4\) , \( -6 a^{2} - 2 a + 16\bigr] \)
${y}^2={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-a^{2}+4\right){x}-6a^{2}-2a+16$
64.7-c2
64.7-c
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
64.7
\( 2^{6} \)
\( 2^{10} \)
$3.17696$
$(-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$28.28981181$
0.795713124
\( 342336 a^{2} + 460416 a - 292544 \)
\( \bigl[a^{2} + a - 2\) , \( a - 1\) , \( a + 1\) , \( -71 a^{2} + 42 a + 312\) , \( 7259 a^{2} - 3836 a - 30834\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-71a^{2}+42a+312\right){x}+7259a^{2}-3836a-30834$
64.7-e1
64.7-e
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
64.7
\( 2^{6} \)
\( 2^{10} \)
$3.17696$
$(-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.051249936$
$265.0243926$
1.146111581
\( 342336 a^{2} + 460416 a - 292544 \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 4\) , \( a^{2} - 3\) , \( -73 a^{2} + 41 a + 315\) , \( -7157 a^{2} + 3791 a + 30416\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-73a^{2}+41a+315\right){x}-7157a^{2}+3791a+30416$
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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.