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-a3
17.3-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.3
\( 17 \)
\( 17^{6} \)
$1.28960$
$(a^2-2a-3)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$109.5689285$
0.507263558
\( -\frac{1205291961947619}{24137569} a^{2} + \frac{418603459872780}{24137569} a + \frac{3470563089465552}{24137569} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 1\) , \( a\) , \( 1773 a^{2} - 589 a - 5152\) , \( -46301 a^{2} + 16115 a + 133250\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(1773a^{2}-589a-5152\right){x}-46301a^{2}+16115a+133250$
153.3-a3
153.3-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.3
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{6} \)
$1.85993$
$(-a^2+1), (a^2-2a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B.1.2
$1$
\( 2^{3} \)
$1$
$18.78534723$
1.043630401
\( -\frac{1205291961947619}{24137569} a^{2} + \frac{418603459872780}{24137569} a + \frac{3470563089465552}{24137569} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a^{2} + a - 2\) , \( 888 a^{2} - 309 a - 2559\) , \( 17706 a^{2} - 6150 a - 50984\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(888a^{2}-309a-2559\right){x}+17706a^{2}-6150a-50984$
289.5-b3
289.5-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.5
\( 17^{2} \)
\( 17^{12} \)
$2.06791$
$(a^2-2a-3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2^{2} \)
$2.409343081$
$7.146850292$
1.434934525
\( -\frac{1205291961947619}{24137569} a^{2} + \frac{418603459872780}{24137569} a + \frac{3470563089465552}{24137569} \)
\( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( 8442 a^{2} - 2777 a - 24583\) , \( 498266 a^{2} - 172595 a - 1435531\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8442a^{2}-2777a-24583\right){x}+498266a^{2}-172595a-1435531$
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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.