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
17.1-a7
17.1-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.1
\( 17 \)
\( 17^{3} \)
$1.28960$
$(2a^2-a-3)$
0
$\Z/12\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3 \)
$1$
$219.1378571$
0.507263558
\( -\frac{170514783}{4913} a^{2} + \frac{42561684}{4913} a + \frac{469465740}{4913} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 44 a^{2} - 16 a - 126\) , \( -207 a^{2} + 71 a + 595\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(44a^{2}-16a-126\right){x}-207a^{2}+71a+595$
153.1-a7
153.1-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.1
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{3} \)
$1.85993$
$(-a^2+1), (2a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$18.78534723$
1.043630401
\( -\frac{170514783}{4913} a^{2} + \frac{42561684}{4913} a + \frac{469465740}{4913} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( 1\) , \( a^{2} - 2 a - 4\) , \( 2 a^{2} - a - 7\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(a^{2}-2a-4\right){x}+2a^{2}-a-7$
289.4-b3
289.4-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.4
\( 17^{2} \)
\( 17^{9} \)
$2.06791$
$(2a^2-a-3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1.204671540$
$14.29370058$
1.434934525
\( -\frac{170514783}{4913} a^{2} + \frac{42561684}{4913} a + \frac{469465740}{4913} \)
\( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( 263 a^{2} - 90 a - 744\) , \( -2482 a^{2} + 872 a + 7144\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(263a^{2}-90a-744\right){x}-2482a^{2}+872a+7144$
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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.