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
289.2-a3
289.2-a
$4$
$4$
\(\Q(\sqrt{-67}) \)
$2$
$[0, 1]$
289.2
\( 17^{2} \)
\( 17^{4} \)
$3.01579$
$(-a), (a-1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$4.511036889$
$4.247877398$
2.341051409
\( \frac{20346417}{289} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \)
${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$
4913.2-a3
4913.2-a
$4$
$4$
\(\Q(\sqrt{-67}) \)
$2$
$[0, 1]$
4913.2
\( 17^{3} \)
\( 17^{10} \)
$6.12368$
$(-a), (a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$16$
\( 2^{3} \)
$1$
$1.030261599$
2.013863795
\( \frac{20346417}{289} \)
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -8 a + 105\) , \( -54 a - 154\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^3+{x}^2+\left(-8a+105\right){x}-54a-154$
4913.3-a3
4913.3-a
$4$
$4$
\(\Q(\sqrt{-67}) \)
$2$
$[0, 1]$
4913.3
\( 17^{3} \)
\( 17^{10} \)
$6.12368$
$(-a), (a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$16$
\( 2^{3} \)
$1$
$1.030261599$
2.013863795
\( \frac{20346417}{289} \)
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 8 a + 97\) , \( 46 a - 305\bigr] \)
${y}^2+a{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(8a+97\right){x}+46a-305$
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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.