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-a1
8.1-a
$4$
$21$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
8.1
\( 2^{3} \)
\( - 2^{9} \)
$1.13736$
$(2)$
0
$\Z/21\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3, 7$
3B.1.1 , 7B.1.1
$1$
\( 3 \)
$1$
$386.8008344$
0.292366465
\( -\frac{140625}{8} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 2\) , \( 13 a^{2} + 2 a - 44\) , \( -22 a^{2} - 3 a + 88\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(13a^{2}+2a-44\right){x}-22a^{2}-3a+88$
72.1-a2
72.1-a
$4$
$21$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( - 2^{9} \cdot 3^{6} \)
$1.64035$
$(-a^2+1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 7$
3B.1.2 , 7B.6.1
$1$
\( 1 \)
$1$
$7.322648121$
0.813627569
\( -\frac{140625}{8} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( a\) , \( 7 a^{2} - 4 a - 23\) , \( 19 a^{2} - 7 a - 56\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(7a^{2}-4a-23\right){x}+19a^{2}-7a-56$
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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.