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
72.1-b4
72.1-b
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$2.44182$
$(-3a-14), (-a+5), (a+5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$22.73403407$
1.211728087
\( \frac{1556068}{81} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -3\) , \( -3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-3{x}-3$
72.1-d4
72.1-d
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$2.44182$
$(-3a-14), (-a+5), (a+5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1.416159776$
$9.301119475$
2.808252391
\( \frac{1556068}{81} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 100667 a - 472156\) , \( 36137766 a - 169501137\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(100667a-472156\right){x}+36137766a-169501137$
144.1-g4
144.1-g
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
144.1
\( 2^{4} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$2.90383$
$(-3a-14), (-a+5), (a+5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{5} \)
$1.617274427$
$9.301119475$
6.414127636
\( \frac{1556068}{81} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( -16\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-7{x}-16$
144.1-j4
144.1-j
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
144.1
\( 2^{4} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$2.90383$
$(-3a-14), (-a+5), (a+5)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{5} \)
$2.502171706$
$22.73403407$
6.063903471
\( \frac{1556068}{81} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( 100667 a - 472160\) , \( -35735098 a + 167612473\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(100667a-472160\right){x}-35735098a+167612473$
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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.