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-b1
162.1-b
$3$
$9$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{2} \cdot 3^{6} \)
$2.46941$
$(2,a+1), (3,a)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 2 \)
$1$
$39.86878607$
1.143786255
\( -\frac{132651}{2} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$
162.1-c1
162.1-c
$3$
$9$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{2} \cdot 3^{6} \)
$2.46941$
$(2,a+1), (3,a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2 \cdot 3 \)
$1$
$3.185925848$
2.467807550
\( -\frac{132651}{2} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -6\) , \( -8\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-6{x}-8$
162.1-e1
162.1-e
$3$
$9$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{14} \cdot 3^{6} \)
$2.46941$
$(2,a+1), (3,a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2 \cdot 3 \)
$0.077107140$
$39.86878607$
4.762480698
\( -\frac{132651}{2} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -99 a - 381\) , \( 822 a + 3183\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-99a-381\right){x}+822a+3183$
162.1-f1
162.1-f
$3$
$9$
\(\Q(\sqrt{15}) \)
$2$
$[2, 0]$
162.1
\( 2 \cdot 3^{4} \)
\( 2^{14} \cdot 3^{6} \)
$2.46941$
$(2,a+1), (3,a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 2 \)
$2.936556370$
$3.185925848$
4.831237322
\( -\frac{132651}{2} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -100 a - 389\) , \( -1415 a - 5483\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-100a-389\right){x}-1415a-5483$
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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.