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
73.2-a1
73.2-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
73.2
\( 73 \)
\( 73^{3} \)
$0.45241$
$(9a-8)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1[2]
$1$
\( 3 \)
$1$
$3.242334089$
0.311993743
\( -\frac{60988685561}{389017} a - \frac{108786941280}{389017} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -4 a + 14\) , \( 16 a - 6\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+14\right){x}+16a-6$
73.2-a2
73.2-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
73.2
\( 73 \)
\( 73^{2} \)
$0.45241$
$(9a-8)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2 \)
$1$
$4.863501133$
0.311993743
\( \frac{927841113}{5329} a - \frac{1323774856}{5329} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -6 a - 1\) , \( 4 a\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-1\right){x}+4a$
73.2-a3
73.2-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
73.2
\( 73 \)
\( 73 \)
$0.45241$
$(9a-8)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1[2]
$1$
\( 1 \)
$1$
$9.727002267$
0.311993743
\( -\frac{9927}{73} a + \frac{30887}{73} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-1\right){x}$
73.2-a4
73.2-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
73.2
\( 73 \)
\( 73^{6} \)
$0.45241$
$(9a-8)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2 \cdot 3 \)
$1$
$1.621167044$
0.311993743
\( \frac{55816089234767}{151334226289} a + \frac{51536736771337}{151334226289} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -9 a + 14\) , \( 30 a - 24\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a+14\right){x}+30a-24$
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Pari/GP
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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.