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
17.2-a7
17.2-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.2
\( 17 \)
\( 17 \)
$1.28960$
$(a^2+a-3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 1 \)
$1$
$73.04595237$
0.507263558
\( \frac{90963}{17} a^{2} + \frac{128385}{17} a + \frac{12528}{17} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( a^{2}\) , \( 0\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+a^{2}{x}$
153.2-a3
153.2-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.2
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17 \)
$1.85993$
$(-a^2+1), (a^2+a-3)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$169.0681251$
1.043630401
\( \frac{90963}{17} a^{2} + \frac{128385}{17} a + \frac{12528}{17} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 1\) , \( a^{2} - 2\) , \( 3 a^{2} - 4 a - 4\) , \( 2 a^{2} - 3 a - 2\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(3a^{2}-4a-4\right){x}+2a^{2}-3a-2$
289.6-b8
289.6-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.6
\( 17^{2} \)
\( 17^{7} \)
$2.06791$
$(a^2+a-3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.401557180$
$42.88110175$
1.434934525
\( \frac{90963}{17} a^{2} + \frac{128385}{17} a + \frac{12528}{17} \)
\( \bigl[1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 1\) , \( 2 a^{2} - 5 a - 1\) , \( -2 a - 1\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(2a^{2}-5a-1\right){x}-2a-1$
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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.