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-b3
72.1-b
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{4} \)
$2.44182$
$(-3a-14), (-a+5), (a+5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$22.73403407$
1.211728087
\( \frac{35152}{9} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 2\) , \( 2\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+2{x}+2$
72.1-d3
72.1-d
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{4} \)
$2.44182$
$(-3a-14), (-a+5), (a+5)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$2.832319552$
$37.20447790$
2.808252391
\( \frac{35152}{9} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 17927 a - 84071\) , \( -2074079 a + 9728303\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(17927a-84071\right){x}-2074079a+9728303$
144.1-g3
144.1-g
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
144.1
\( 2^{4} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{4} \)
$2.90383$
$(-3a-14), (-a+5), (a+5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$3.234548855$
$37.20447790$
6.414127636
\( \frac{35152}{9} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( -1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-2{x}-1$
144.1-j3
144.1-j
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
144.1
\( 2^{4} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{4} \)
$2.90383$
$(-3a-14), (-a+5), (a+5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$5.004343412$
$22.73403407$
6.063903471
\( \frac{35152}{9} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( 17927 a - 84075\) , \( 2145787 a - 10064627\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(17927a-84075\right){x}+2145787a-10064627$
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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.