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
171.2-a1
171.2-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
171.2
\( 3^{2} \cdot 19 \)
\( 3^{9} \cdot 19^{3} \)
$0.55969$
$(-2a+1), (-5a+2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2 \cdot 3 \)
$1$
$2.713137527$
0.522143560
\( -\frac{29840721}{6859} a - \frac{5426511}{6859} \)
\( \bigl[1\) , \( -1\) , \( a\) , \( 4 a - 9\) , \( -10 a + 13\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(4a-9\right){x}-10a+13$
171.2-a2
171.2-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
171.2
\( 3^{2} \cdot 19 \)
\( 3^{9} \cdot 19^{6} \)
$0.55969$
$(-2a+1), (-5a+2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2^{2} \cdot 3 \)
$1$
$1.356568763$
0.522143560
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \)
\( \bigl[1\) , \( -1\) , \( a\) , \( 19 a + 6\) , \( -19 a + 67\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(19a+6\right){x}-19a+67$
171.2-a3
171.2-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
171.2
\( 3^{2} \cdot 19 \)
\( 3^{3} \cdot 19 \)
$0.55969$
$(-2a+1), (-5a+2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2 \)
$1$
$8.139412583$
0.522143560
\( \frac{9153}{19} a + \frac{27648}{19} \)
\( \bigl[1\) , \( -1\) , \( a\) , \( -a + 1\) , \( 0\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a+1\right){x}$
171.2-a4
171.2-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
171.2
\( 3^{2} \cdot 19 \)
\( 3^{3} \cdot 19^{2} \)
$0.55969$
$(-2a+1), (-5a+2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2^{2} \)
$1$
$4.069706291$
0.522143560
\( \frac{363527109}{361} a - \frac{76135923}{361} \)
\( \bigl[1\) , \( -1\) , \( a\) , \( -6 a + 11\) , \( 10 a + 1\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-6a+11\right){x}+10a+1$
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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.