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-a6
17.2-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.2
\( 17 \)
\( 17^{2} \)
$1.28960$
$(a^2+a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B.1.2
$1$
\( 2 \)
$1$
$36.52297618$
0.507263558
\( \frac{41241472785}{289} a^{2} + \frac{78376016664}{289} a + \frac{23273565192}{289} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -4 a^{2}\) , \( -7 a^{2} - 13 a - 4\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}-4a^{2}{x}-7a^{2}-13a-4$
153.2-a2
153.2-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.2
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{2} \)
$1.85993$
$(-a^2+1), (a^2+a-3)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{3} \)
$1$
$169.0681251$
1.043630401
\( \frac{41241472785}{289} a^{2} + \frac{78376016664}{289} a + \frac{23273565192}{289} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 1\) , \( a^{2} - 2\) , \( -2 a^{2} + 6 a - 9\) , \( -9 a^{2} + 10 a + 14\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-2a^{2}+6a-9\right){x}-9a^{2}+10a+14$
289.6-b7
289.6-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.6
\( 17^{2} \)
\( 17^{8} \)
$2.06791$
$(a^2+a-3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2^{2} \)
$0.803114360$
$21.44055087$
1.434934525
\( \frac{41241472785}{289} a^{2} + \frac{78376016664}{289} a + \frac{23273565192}{289} \)
\( \bigl[1\) , \( -a^{2} - a + 1\) , \( a^{2} + a - 1\) , \( -23 a^{2} - 10 a - 6\) , \( -41 a^{2} - 72 a - 17\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-23a^{2}-10a-6\right){x}-41a^{2}-72a-17$
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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.