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-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
\( -\frac{132651}{2} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$
1296.1-c1
1296.1-c
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1296.1
\( 2^{4} \cdot 3^{4} \)
\( 2^{14} \cdot 3^{12} \)
$1.85729$
$(a+1), (a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$1$
$3.253446840$
1.878378408
\( -\frac{132651}{2} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -36\) , \( -72 a\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}-36{x}-72a$
1296.1-f1
1296.1-f
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1296.1
\( 2^{4} \cdot 3^{4} \)
\( 2^{14} \cdot 3^{12} \)
$1.85729$
$(a+1), (a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$1$
$3.253446840$
1.878378408
\( -\frac{132651}{2} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -a - 38\) , \( 34 a - 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-38\right){x}+34a-1$
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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.