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-a1
17.2-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
17.2
\( 17 \)
\( 17 \)
$0.65422$
$(a-5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$22.24460707$
0.685504883
\( -\frac{4096}{17} a - \frac{16384}{17} \)
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -a - 1\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-a-1\right){x}$
17.2-a2
17.2-a
$2$
$3$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
17.2
\( 17 \)
\( 17^{3} \)
$0.65422$
$(a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$2.471623008$
0.685504883
\( \frac{2659135311872}{4913} a - \frac{6123387461632}{4913} \)
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 9 a + 9\) , \( -13 a - 20\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(9a+9\right){x}-13a-20$
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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.