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-b5
72.1-b
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$2.44182$
$(-3a-14), (-a+5), (a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2 \)
$1$
$5.683508517$
1.211728087
\( \frac{28756228}{3} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -13\) , \( -55\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-13{x}-55$
72.1-d5
72.1-d
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$2.44182$
$(-3a-14), (-a+5), (a+5)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1.416159776$
$37.20447790$
2.808252391
\( \frac{28756228}{3} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -266147 a - 1248326\) , \( 161273084 a + 756437825\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-266147a-1248326\right){x}+161273084a+756437825$
144.1-g5
144.1-g
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
144.1
\( 2^{4} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$2.90383$
$(-3a-14), (-a+5), (a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$1.617274427$
$37.20447790$
6.414127636
\( \frac{28756228}{3} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -17\) , \( -4\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-17{x}-4$
144.1-j5
144.1-j
$6$
$8$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
144.1
\( 2^{4} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{2} \)
$2.90383$
$(-3a-14), (-a+5), (a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$10.00868682$
$5.683508517$
6.063903471
\( \frac{28756228}{3} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -266147 a - 1248330\) , \( -162337672 a - 761431169\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-266147a-1248330\right){x}-162337672a-761431169$
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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.