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-a3
17.2-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.2
\( 17 \)
\( 17^{6} \)
$1.28960$
$(a^2+a-3)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$109.5689285$
0.507263558
\( \frac{786688502074839}{24137569} a^{2} - \frac{1205291961947619}{24137569} a - \frac{513397838579364}{24137569} \)
\( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -475 a^{2} + 733 a + 296\) , \( 7691 a^{2} - 11788 a - 5014\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-475a^{2}+733a+296\right){x}+7691a^{2}-11788a-5014$
153.2-a7
153.2-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.2
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{6} \)
$1.85993$
$(-a^2+1), (a^2+a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B.1.2
$1$
\( 2^{3} \)
$1$
$18.78534723$
1.043630401
\( \frac{786688502074839}{24137569} a^{2} - \frac{1205291961947619}{24137569} a - \frac{513397838579364}{24137569} \)
\( \bigl[a + 1\) , \( -a\) , \( a^{2} + a - 1\) , \( -90 a^{2} + 154 a + 22\) , \( -863 a^{2} + 1357 a + 493\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}-a{x}^{2}+\left(-90a^{2}+154a+22\right){x}-863a^{2}+1357a+493$
289.6-b3
289.6-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.6
\( 17^{2} \)
\( 17^{12} \)
$2.06791$
$(a^2+a-3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2^{2} \)
$2.409343081$
$7.146850292$
1.434934525
\( \frac{786688502074839}{24137569} a^{2} - \frac{1205291961947619}{24137569} a - \frac{513397838579364}{24137569} \)
\( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( -2234 a^{2} + 3503 a + 1323\) , \( -84599 a^{2} + 129898 a + 54699\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2234a^{2}+3503a+1323\right){x}-84599a^{2}+129898a+54699$
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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.