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-a1
17.2-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.2
\( 17 \)
\( 17^{3} \)
$1.28960$
$(a^2+a-3)$
0
$\Z/12\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3 \)
$1$
$219.1378571$
0.507263558
\( \frac{42561684}{4913} a^{2} + \frac{127953099}{4913} a + \frac{43312806}{4913} \)
\( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -30 a^{2} + 43 a + 21\) , \( 103 a^{2} - 160 a - 66\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-30a^{2}+43a+21\right){x}+103a^{2}-160a-66$
153.2-a6
153.2-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.2
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{3} \)
$1.85993$
$(-a^2+1), (a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$18.78534723$
1.043630401
\( \frac{42561684}{4913} a^{2} + \frac{127953099}{4913} a + \frac{43312806}{4913} \)
\( \bigl[a + 1\) , \( -a\) , \( a^{2} + a - 1\) , \( -10 a^{2} + 9 a + 12\) , \( -15 a^{2} + 24 a + 3\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}-a{x}^{2}+\left(-10a^{2}+9a+12\right){x}-15a^{2}+24a+3$
289.6-b1
289.6-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.6
\( 17^{2} \)
\( 17^{9} \)
$2.06791$
$(a^2+a-3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1.204671540$
$14.29370058$
1.434934525
\( \frac{42561684}{4913} a^{2} + \frac{127953099}{4913} a + \frac{43312806}{4913} \)
\( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( -149 a^{2} + 223 a + 123\) , \( -1345 a^{2} + 2090 a + 839\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-149a^{2}+223a+123\right){x}-1345a^{2}+2090a+839$
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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.