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-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-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
\( -\frac{1167051}{512} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -15\) , \( -30\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-15{x}-30$
1296.1-c2
1296.1-c
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1296.1
\( 2^{4} \cdot 3^{4} \)
\( 2^{30} \cdot 3^{4} \)
$1.85729$
$(a+1), (a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$1$
$3.253446840$
1.878378408
\( -\frac{1167051}{512} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -18\) , \( 26 a\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-18{x}+26a$
1296.1-f2
1296.1-f
$3$
$9$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
1296.1
\( 2^{4} \cdot 3^{4} \)
\( 2^{30} \cdot 3^{4} \)
$1.85729$
$(a+1), (a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$1$
$3.253446840$
1.878378408
\( -\frac{1167051}{512} \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -18\) , \( -26 a\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}-18{x}-26a$
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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.