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
27.1-a1
27.1-a
$4$
$27$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
27.1
\( 3^{3} \)
\( - 3^{9} \)
$1.39297$
$(-a^2+1)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-27$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.2
$1$
\( 3 \)
$1$
$1.837900525$
0.612633508
\( -12288000 \)
\( \bigl[0\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( 280 a^{2} - 89 a - 818\) , \( 2805 a^{2} - 963 a - 8098\bigr] \)
${y}^2+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(280a^{2}-89a-818\right){x}+2805a^{2}-963a-8098$
27.1-a3
27.1-a
$4$
$27$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
27.1
\( 3^{3} \)
\( - 3^{3} \)
$1.39297$
$(-a^2+1)$
0
$\Z/9\Z$
$\textsf{potential}$
$-27$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$446.6098277$
0.612633508
\( -12288000 \)
\( \bigl[0\) , \( a^{2} - 1\) , \( a + 1\) , \( 17 a^{2} - 3 a - 53\) , \( -56 a^{2} + 17 a + 164\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(17a^{2}-3a-53\right){x}-56a^{2}+17a+164$
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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.