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
324.1-a1
324.1-a
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{2} \cdot 3^{12} \)
$1.73734$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$1$
$6.506893680$
1.419920610
\( -\frac{132651}{2} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -11 a - 19\) , \( 26 a + 44\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a-19\right){x}+26a+44$
324.1-b1
324.1-b
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{2} \cdot 3^{6} \)
$1.73734$
$(-a+2), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 3 \)
$1$
$39.86878607$
2.900027461
\( -\frac{132651}{2} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-3{x}+3$
324.1-c1
324.1-c
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{2} \cdot 3^{12} \)
$1.73734$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$1$
$6.506893680$
1.419920610
\( -\frac{132651}{2} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 9 a - 30\) , \( -27 a + 70\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(9a-30\right){x}-27a+70$
324.1-d1
324.1-d
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{2} \cdot 3^{6} \)
$1.73734$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$3.185925848$
0.695226017
\( -\frac{132651}{2} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 15 a - 42\) , \( 72 a - 201\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(15a-42\right){x}+72a-201$
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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.