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-a6
17.1-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
17.1
\( 17 \)
\( 17^{6} \)
$1.28960$
$(2a^2-a-3)$
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
\( \frac{418603459872780}{24137569} a^{2} + \frac{786688502074839}{24137569} a + \frac{222772245824754}{24137569} \)
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} + a - 2\) , \( 79 a^{2} - 26 a - 231\) , \( 122 a^{2} - 44 a - 351\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(79a^{2}-26a-231\right){x}+122a^{2}-44a-351$
153.1-a6
153.1-a
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
153.1
\( 3^{2} \cdot 17 \)
\( 3^{6} \cdot 17^{6} \)
$1.85993$
$(-a^2+1), (2a^2-a-3)$
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
\( \frac{418603459872780}{24137569} a^{2} + \frac{786688502074839}{24137569} a + \frac{222772245824754}{24137569} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( 1\) , \( -4 a^{2} - 7 a - 9\) , \( -12 a^{2} - 18 a - 6\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-4a^{2}-7a-9\right){x}-12a^{2}-18a-6$
289.4-b2
289.4-b
$8$
$12$
\(\Q(\zeta_{9})^+\)
$3$
$[3, 0]$
289.4
\( 17^{2} \)
\( 17^{12} \)
$2.06791$
$(2a^2-a-3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2^{2} \)
$2.409343081$
$7.146850292$
1.434934525
\( \frac{418603459872780}{24137569} a^{2} + \frac{786688502074839}{24137569} a + \frac{222772245824754}{24137569} \)
\( \bigl[a^{2} + a - 1\) , \( a + 1\) , \( a\) , \( 458 a^{2} - 135 a - 1349\) , \( 2448 a^{2} - 806 a - 7118\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(458a^{2}-135a-1349\right){x}+2448a^{2}-806a-7118$
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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.