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-a2
27.1-a
$4$
$27$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
27.1
\( 3^{3} \)
\( - 3^{3} \)
$1.39297$
$(-a^2+1)$
0
$\Z/3\Z$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 1 \)
$1$
$49.62331419$
0.612633508
\( 0 \)
\( \bigl[0\) , \( a^{2} + a - 2\) , \( a^{2} - 1\) , \( a + 2\) , \( 12 a^{2} - 4 a - 35\bigr] \)
${y}^2+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a+2\right){x}+12a^{2}-4a-35$
27.1-a4
27.1-a
$4$
$27$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
27.1
\( 3^{3} \)
\( - 3^{9} \)
$1.39297$
$(-a^2+1)$
0
$\Z/9\Z$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 3 \)
$1$
$148.8699425$
0.612633508
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}$
576.1-a2
576.1-a
$4$
$6$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( - 2^{12} \cdot 3^{3} \)
$2.31980$
$(-a^2+1), (2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$24.81165709$
1.378425394
\( 0 \)
\( \bigl[0\) , \( a^{2} + a - 2\) , \( 0\) , \( a + 2\) , \( 48 a^{2} - 16 a - 138\bigr] \)
${y}^2={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(a+2\right){x}+48a^{2}-16a-138$
576.1-a4
576.1-a
$4$
$6$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( - 2^{12} \cdot 3^{9} \)
$2.31980$
$(-a^2+1), (2)$
0
$\Z/6\Z$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$74.43497128$
1.378425394
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \)
${y}^2={x}^{3}+1$
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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.