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
162.1-a1
162.1-a
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{2} \cdot 3^{6} \)
$1.10435$
$(a+1), (a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$1$
$3.185925848$
1.839395146
\( -\frac{132651}{2} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \)
${y}^2+a{x}{y}={x}^{3}-3{x}-3$
162.1-a2
162.1-a
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{18} \cdot 3^{10} \)
$1.10435$
$(a+1), (a)$
0
$\Z/9\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3^{3} \)
$1$
$9.557777544$
1.839395146
\( -\frac{1167051}{512} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-14{x}+29$
162.1-a3
162.1-a
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{6} \cdot 3^{6} \)
$1.10435$
$(a+1), (a)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1$
$9.557777544$
1.839395146
\( \frac{9261}{8} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$
162.1-b1
162.1-b
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{2} \cdot 3^{6} \)
$1.10435$
$(a+1), (a)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$0.077107140$
$39.86878607$
1.183247842
\( -\frac{132651}{2} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$
162.1-b2
162.1-b
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{18} \cdot 3^{10} \)
$1.10435$
$(a+1), (a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$0.693964260$
$1.476621706$
1.183247842
\( -\frac{1167051}{512} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -15\) , \( -30\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-15{x}-30$
162.1-b3
162.1-b
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{6} \cdot 3^{6} \)
$1.10435$
$(a+1), (a)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$0.231321420$
$13.28959535$
1.183247842
\( \frac{9261}{8} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 0\) , \( 0\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}$
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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.