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
8.1-a2 8.1-a $4$
$21$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
8.1
\( 2^{3} \)
\( - 2^{63} \)
$1.13736$
$(2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3, 7$
3B.1.1 , 7B.1.3 $1$
\( 3 \cdot 7 \)
$1$
$1.127699225$
0.292366465
\( -\frac{1159088625}{2097152} \)
\( \bigl[a\) , \( -1\) , \( a^{2} - 1\) , \( 125040 a^{2} - 43189 a - 360486\) , \( 56242078 a^{2} - 19527401 a - 161952511\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-1\right){y}={x}^{3}-{x}^{2}+\left(125040a^{2}-43189a-360486\right){x}+56242078a^{2}-19527401a-161952511$
72.1-a3 72.1-a $4$
$21$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( - 2^{63} \cdot 3^{6} \)
$1.64035$
$(-a^2+1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3, 7$
3B.1.2 , 7B.6.3 $1$
\( 1 \)
$1$
$7.322648121$
0.813627569
\( -\frac{1159088625}{2097152} \)
\( \bigl[a\) , \( a + 1\) , \( a^{2} - 1\) , \( 62084 a^{2} - 21557 a - 178770\) , \( -19632547 a^{2} + 6818300 a + 56529689\bigr] \) ${y}^2+a{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(62084a^{2}-21557a-178770\right){x}-19632547a^{2}+6818300a+56529689$
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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.
