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-b1
288.1-b
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
288.1
\( 2^{5} \cdot 3^{2} \)
\( 2^{6} \cdot 3^{8} \)
$1.04119$
$(a), (3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.337900933$
$10.97780010$
1.311474095
\( \frac{97336}{81} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( 2\) , \( 1\bigr] \)
${y}^2+a{x}{y}={x}^{3}+2{x}+1$
288.1-c1
288.1-c
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
288.1
\( 2^{5} \cdot 3^{2} \)
\( 2^{6} \cdot 3^{8} \)
$1.04119$
$(a), (3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$8.017247373$
1.417262496
\( \frac{97336}{81} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 2\) , \( -1\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}-1$
2304.1-a1
2304.1-a
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2304.1
\( 2^{8} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{8} \)
$1.75107$
$(a), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.690728597$
1.658422999
\( \frac{97336}{81} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 16 a + 24\) , \( 40 a + 56\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(16a+24\right){x}+40a+56$
2304.1-t1
2304.1-t
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2304.1
\( 2^{8} \cdot 3^{2} \)
\( 2^{18} \cdot 3^{8} \)
$1.75107$
$(a), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.690728597$
1.658422999
\( \frac{97336}{81} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a + 24\) , \( -40 a - 56\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(16a+24\right){x}-40a-56$
2592.1-a1
2592.1-a
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2592.1
\( 2^{5} \cdot 3^{4} \)
\( 2^{6} \cdot 3^{20} \)
$1.80340$
$(a), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.620169672$
$2.672415791$
2.343848582
\( \frac{97336}{81} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 17\) , \( -10\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+17{x}-10$
2592.1-e1
2592.1-e
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
2592.1
\( 2^{5} \cdot 3^{4} \)
\( 2^{6} \cdot 3^{20} \)
$1.80340$
$(a), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.659266702$
2.587492299
\( \frac{97336}{81} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 18\) , \( 27\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+18{x}+27$
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Pari/GP
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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.