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
171.1-a1
171.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
171.1
\( 3^{2} \cdot 19 \)
\( 3^{9} \cdot 19^{3} \)
$0.55969$
$(-2a+1), (-5a+3)$
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
\( \frac{29840721}{6859} a - \frac{35267232}{6859} \)
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a - 5\) , \( 9 a + 3\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5a-5\right){x}+9a+3$
171.1-a2
171.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
171.1
\( 3^{2} \cdot 19 \)
\( 3^{9} \cdot 19^{6} \)
$0.55969$
$(-2a+1), (-5a+3)$
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
\( -\frac{36038181633}{47045881} a - \frac{39546962313}{47045881} \)
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -20 a + 25\) , \( 18 a + 48\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-20a+25\right){x}+18a+48$
171.1-a3
171.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
171.1
\( 3^{2} \cdot 19 \)
\( 3^{3} \cdot 19 \)
$0.55969$
$(-2a+1), (-5a+3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2 \)
$1$
$8.139412583$
0.522143560
\( -\frac{9153}{19} a + \frac{36801}{19} \)
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 0\) , \( -a\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-a$
171.1-a4
171.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
171.1
\( 3^{2} \cdot 19 \)
\( 3^{3} \cdot 19^{2} \)
$0.55969$
$(-2a+1), (-5a+3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1[2]
$1$
\( 2^{2} \)
$1$
$4.069706291$
0.522143560
\( -\frac{363527109}{361} a + \frac{287391186}{361} \)
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5 a + 5\) , \( -11 a + 11\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(5a+5\right){x}-11a+11$
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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.