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
20736.1-CMd1 20736.1-CMd $1$
$1$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
20736.1
\( 2^{8} \cdot 3^{4} \)
\( 2^{16} \cdot 3^{6} \)
$1.85729$
$(-2a+1), (2)$
$2$
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$ ✓
✓
✓
$1$
\( 2^{2} \cdot 3 \)
$0.016899059$
$3.217911259$
3.014027543
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -4\bigr] \) ${y}^2={x}^{3}-4$
2916.1-b1 2916.1-b $2$
$3$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
2916.1
\( 2^{2} \cdot 3^{6} \)
\( 2^{4} \cdot 3^{6} \)
$1.31330$
$(a+1), (3)$
$1$
$\Z/3\Z$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$ ✓
✓
✓
$3$
3B.1.1 $1$
\( 3 \)
$0.450320685$
$6.435822518$
1.932122672
\( 0 \)
\( \bigl[0\) , \( 0\) , \( i + 1\) , \( 0\) , \( -i\bigr] \) ${y}^2+\left(i+1\right){y}={x}^{3}-i$
11664.4-i1 11664.4-i $2$
$3$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
11664.4
\( 2^{4} \cdot 3^{6} \)
\( 2^{4} \cdot 3^{6} \)
$2.62661$
$(a), (-a-1), (a-1)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$ ✓
✓
✓
$1$
\( 1 \)
$0.450320685$
$6.435822518$
4.098651131
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 1\bigr] \) ${y}^2+a{y}={x}^{3}+1$
324.1-a2 324.1-a $2$
$3$
\(\Q(\sqrt{-21}) \) $2$
$[0, 1]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{16} \cdot 3^{6} \)
$3.47468$
$(2,a+1), (3,a)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$ ✓
✓
✓
$1$
\( 3 \)
$0.450320685$
$6.435822518$
3.794613599
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -4\bigr] \) ${y}^2={x}^3-4$
324.1-a1 324.1-a $2$
$3$
\(\Q(\sqrt{3}) \) $2$
$[2, 0]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{4} \cdot 3^{6} \)
$1.31330$
$(a+1), (a)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$ ✓
✓
✓
$3$
3B.1.2 $1$
\( 1 \)
$0.450320685$
$7.431447726$
1.932122672
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -8 a - 14\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-8a-14$
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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.
