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
289.1-a1
289.1-a
$4$
$4$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
289.1
\( 17^{2} \)
\( 17^{8} \)
$4.70389$
$(17)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.123938699$
0.083179859
\( -\frac{35937}{83521} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \)
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$
289.1-a2
289.1-a
$4$
$4$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
289.1
\( 17^{2} \)
\( 17^{2} \)
$4.70389$
$(17)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$1$
$8.495754796$
0.083179859
\( \frac{35937}{17} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$
289.1-a3
289.1-a
$4$
$4$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
289.1
\( 17^{2} \)
\( 17^{4} \)
$4.70389$
$(17)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$4.247877398$
0.083179859
\( \frac{20346417}{289} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \)
${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$
289.1-a4
289.1-a
$4$
$4$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
289.1
\( 17^{2} \)
\( 17^{2} \)
$4.70389$
$(17)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$1$
$2.123938699$
0.083179859
\( \frac{82483294977}{17} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \)
${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.