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-a1
17.1-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
17.1
\( 17 \)
\( - 17^{2} \)
$1.32096$
$(a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$24.46621578$
1.680346598
\( -\frac{9844754985}{289} a + \frac{40758297444}{289} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 4 a + 12\) , \( -3 a - 9\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(4a+12\right){x}-3a-9$
17.1-a2
17.1-a
$2$
$2$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
17.1
\( 17 \)
\( 17 \)
$1.32096$
$(a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$48.93243156$
1.680346598
\( -\frac{34263}{17} a + \frac{172989}{17} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -a - 3\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-a-3\right){x}$
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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.