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
73.1-a1
73.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
73.1
\( 73 \)
\( 73^{3} \)
$0.45241$
$(-9a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1[2]
$1$
\( 3 \)
$1$
$3.242334089$
0.311993743
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 6 a + 10\) , \( -11 a + 20\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+10\right){x}-11a+20$
73.1-a2
73.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
73.1
\( 73 \)
\( 73^{2} \)
$0.45241$
$(-9a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2 \)
$1$
$4.863501133$
0.311993743
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \)
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 5\) , \( -4 a + 4\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+5{x}-4a+4$
73.1-a3
73.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
73.1
\( 73 \)
\( 73 \)
$0.45241$
$(-9a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1[2]
$1$
\( 1 \)
$1$
$9.727002267$
0.311993743
\( \frac{9927}{73} a + \frac{20960}{73} \)
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}$
73.1-a4
73.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
73.1
\( 73 \)
\( 73^{6} \)
$0.45241$
$(-9a+1)$
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
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 11 a + 5\) , \( -20 a + 11\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a+5\right){x}-20a+11$
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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.