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
288.1-b4
288.1-b
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
288.1
\( 2^{5} \cdot 3^{2} \)
\( 2^{6} \cdot 3^{2} \)
$1.04119$
$(a), (3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$0.337900933$
$43.91120043$
1.311474095
\( \frac{7301384}{3} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -9\) , \( 7\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-9{x}+7$
288.1-c4
288.1-c
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
288.1
\( 2^{5} \cdot 3^{2} \)
\( 2^{6} \cdot 3^{2} \)
$1.04119$
$(a), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1$
$8.017247373$
1.417262496
\( \frac{7301384}{3} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -9\) , \( -8\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-9{x}-8$
2304.1-a4
2304.1-a
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2304.1
\( 2^{8} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{2} \)
$1.75107$
$(a), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$9.381457194$
1.658422999
\( \frac{7301384}{3} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 64 a - 96\) , \( 300 a - 420\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(64a-96\right){x}+300a-420$
2304.1-t4
2304.1-t
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2304.1
\( 2^{8} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{2} \)
$1.75107$
$(a), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$9.381457194$
1.658422999
\( \frac{7301384}{3} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 64 a - 96\) , \( -300 a + 420\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(64a-96\right){x}-300a+420$
2592.1-a4
2592.1-a
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2592.1
\( 2^{5} \cdot 3^{4} \)
\( 2^{6} \cdot 3^{14} \)
$1.80340$
$(a), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.620169672$
$2.672415791$
2.343848582
\( \frac{7301384}{3} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -72\) , \( -275\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-72{x}-275$
2592.1-e4
2592.1-e
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2592.1
\( 2^{5} \cdot 3^{4} \)
\( 2^{6} \cdot 3^{14} \)
$1.80340$
$(a), (3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$14.63706681$
2.587492299
\( \frac{7301384}{3} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -73\) , \( 202\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-73{x}+202$
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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.