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
5329.1-a1
5329.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
5329.1
\( 73^{2} \)
\( 73^{9} \)
$1.32239$
$(-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{2} \)
$2.486811560$
$0.379486501$
2.179408166
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 553 a + 535\) , \( 9628 a - 12840\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(553a+535\right){x}+9628a-12840$
5329.1-a2
5329.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
5329.1
\( 73^{2} \)
\( 73^{8} \)
$1.32239$
$(-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{2} \)
$1.657874373$
$0.569229752$
2.179408166
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 75 a + 341\) , \( 3389 a - 2532\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(75a+341\right){x}+3389a-2532$
5329.1-a3
5329.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
5329.1
\( 73^{2} \)
\( 73^{7} \)
$1.32239$
$(-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{2} \)
$0.828937186$
$1.138459504$
2.179408166
\( \frac{9927}{73} a + \frac{20960}{73} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -10 a + 26\) , \( 71 a - 95\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a+26\right){x}+71a-95$
5329.1-a4
5329.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
5329.1
\( 73^{2} \)
\( 73^{12} \)
$1.32239$
$(-9a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{2} \)
$4.973623120$
$0.189743250$
2.179408166
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 868 a + 135\) , \( 18504 a - 12861\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(868a+135\right){x}+18504a-12861$
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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.