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
17.3-a4
17.3-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.3
\( 17 \)
\( 17^{3} \)
$1.28960$
$(a^2-2a-3)$
0
$\Z/12\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3 \)
$1$
$219.1378571$
0.507263558
\( \frac{127953099}{4913} a^{2} - \frac{170514783}{4913} a - \frac{127470024}{4913} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 1\) , \( a\) , \( 98 a^{2} - 19 a - 307\) , \( -668 a^{2} + 195 a + 1990\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(98a^{2}-19a-307\right){x}-668a^{2}+195a+1990$
153.3-a4
153.3-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.3
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{3} \)
$1.85993$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$18.78534723$
1.043630401
\( \frac{127953099}{4913} a^{2} - \frac{170514783}{4913} a - \frac{127470024}{4913} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a^{2} + a - 2\) , \( 53 a^{2} - 19 a - 154\) , \( 338 a^{2} - 118 a - 975\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(53a^{2}-19a-154\right){x}+338a^{2}-118a-975$
289.5-b4
289.5-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.5
\( 17^{2} \)
\( 17^{9} \)
$2.06791$
$(a^2-2a-3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1.204671540$
$14.29370058$
1.434934525
\( \frac{127953099}{4913} a^{2} - \frac{170514783}{4913} a - \frac{127470024}{4913} \)
\( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( 457 a^{2} - 72 a - 1463\) , \( 8720 a^{2} - 3561 a - 24091\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(457a^{2}-72a-1463\right){x}+8720a^{2}-3561a-24091$
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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.