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-a1
289.2-a
$6$
$8$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
289.2
\( 17^{2} \)
\( 17^{8} \)
$0.73687$
$(a+4), (a-4)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$0.509074358$
$2.123938699$
0.540621365
\( -\frac{35937}{83521} \)
\( \bigl[i\) , \( 1\) , \( i\) , \( 0\) , \( 14\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+14$
289.2-a2
289.2-a
$6$
$8$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
289.2
\( 17^{2} \)
\( 17^{2} \)
$0.73687$
$(a+4), (a-4)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$0.509074358$
$8.495754796$
0.540621365
\( \frac{35937}{17} \)
\( \bigl[i\) , \( 1\) , \( i\) , \( 0\) , \( 0\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}$
289.2-a3
289.2-a
$6$
$8$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
289.2
\( 17^{2} \)
\( 17^{10} \)
$0.73687$
$(a+4), (a-4)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.254537179$
$1.061969349$
0.540621365
\( -\frac{73070565686415}{6975757441} a + \frac{321713588002536}{6975757441} \)
\( \bigl[i\) , \( 1\) , \( i\) , \( -75 i + 40\) , \( -38 i + 304\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(-75i+40\right){x}-38i+304$
289.2-a4
289.2-a
$6$
$8$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
289.2
\( 17^{2} \)
\( 17^{10} \)
$0.73687$
$(a+4), (a-4)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.254537179$
$1.061969349$
0.540621365
\( \frac{73070565686415}{6975757441} a + \frac{321713588002536}{6975757441} \)
\( \bigl[i\) , \( 1\) , \( i\) , \( 75 i + 40\) , \( 38 i + 304\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+\left(75i+40\right){x}+38i+304$
289.2-a5
289.2-a
$6$
$8$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
289.2
\( 17^{2} \)
\( 17^{4} \)
$0.73687$
$(a+4), (a-4)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1.018148717$
$4.247877398$
0.540621365
\( \frac{20346417}{289} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-6{x}-4$
289.2-a6
289.2-a
$6$
$8$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
289.2
\( 17^{2} \)
\( 17^{2} \)
$0.73687$
$(a+4), (a-4)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 1 \)
$2.036297434$
$2.123938699$
0.540621365
\( \frac{82483294977}{17} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-91{x}-310$
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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.