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
130816.3-a1
130816.3-a
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
130816.3
\( 2^{8} \cdot 7 \cdot 73 \)
\( 2^{26} \cdot 7^{4} \cdot 73^{2} \)
$2.94350$
$(3a-2), (-9a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.999880768$
$0.681293906$
3.146386573
\( \frac{146913674955}{25589858} a - \frac{269643786736}{12794929} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -181 a + 158\) , \( 177 a - 1031\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-181a+158\right){x}+177a-1031$
130816.3-a2
130816.3-a
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
130816.3
\( 2^{8} \cdot 7 \cdot 73 \)
\( 2^{28} \cdot 7^{2} \cdot 73 \)
$2.94350$
$(3a-2), (-9a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.499940384$
$1.362587813$
3.146386573
\( -\frac{20198991}{14308} a + \frac{7397423}{14308} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a - 2\) , \( -47 a - 7\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-21a-2\right){x}-47a-7$
130816.3-b1
130816.3-b
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
130816.3
\( 2^{8} \cdot 7 \cdot 73 \)
\( 2^{26} \cdot 7^{4} \cdot 73^{2} \)
$2.94350$
$(3a-2), (-9a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$1$
$0.681293906$
3.146761764
\( \frac{146913674955}{25589858} a - \frac{269643786736}{12794929} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 158 a + 23\) , \( -177 a + 1031\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(158a+23\right){x}-177a+1031$
130816.3-b2
130816.3-b
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
130816.3
\( 2^{8} \cdot 7 \cdot 73 \)
\( 2^{28} \cdot 7^{2} \cdot 73 \)
$2.94350$
$(3a-2), (-9a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$1.362587813$
3.146761764
\( -\frac{20198991}{14308} a + \frac{7397423}{14308} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a + 23\) , \( 47 a + 7\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+23\right){x}+47a+7$
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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.