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 $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{2} \cdot 3^{10} \)
$0.65665$
$(-2a+1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.1[2] $1$
\( 3 \)
$1$
$1.878378408$
0.722988186
\( -\frac{17268549}{2} a - 114659280 \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 91 a - 62\) , \( -276 a - 13\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(91a-62\right){x}-276a-13$
324.1-a2 324.1-a $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{2} \cdot 3^{10} \)
$0.65665$
$(-2a+1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.1[2] $1$
\( 3 \)
$1$
$1.878378408$
0.722988186
\( \frac{17268549}{2} a - \frac{246587109}{2} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 61 a - 92\) , \( 276 a - 289\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(61a-92\right){x}+276a-289$
324.1-a3 324.1-a $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{2} \cdot 3^{6} \)
$0.65665$
$(-2a+1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1[2] $1$
\( 1 \)
$1$
$5.635135226$
0.722988186
\( -\frac{132651}{2} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -3 a + 3\) , \( 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-3a+3\right){x}+3$
324.1-a4 324.1-a $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{18} \cdot 3^{10} \)
$0.65665$
$(-2a+1), (2)$
0
$\Z/9\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1[2] $1$
\( 3^{3} \)
$1$
$1.878378408$
0.722988186
\( -\frac{1167051}{512} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -14 a + 13\) , \( 29\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-14a+13\right){x}+29$
324.1-a5 324.1-a $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{6} \cdot 3^{6} \)
$0.65665$
$(-2a+1), (2)$
0
$\Z/3\Z\oplus\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3Cs.1.1[2] $1$
\( 3^{2} \)
$1$
$5.635135226$
0.722988186
\( \frac{9261}{8} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( a - 2\) , \( -1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-2\right){x}-1$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
