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-a4
72.1-a
$10$
$32$
\(\Q(\sqrt{2}, \sqrt{3})\)
$4$
$[4, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$7.32059$
$(a^3-4a+1), (a^2-2)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$516.8363050$
1.345927877
\( \frac{35152}{9} \)
\( \bigl[a^{3} - 3 a\) , \( 0\) , \( a^{3} - 3 a\) , \( -2\) , \( -1\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}-2{x}-1$
72.1-b4
72.1-b
$10$
$32$
\(\Q(\sqrt{2}, \sqrt{3})\)
$4$
$[4, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$7.32059$
$(a^3-4a+1), (a^2-2)$
$1$
$\Z/2\Z\oplus\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$0.269818466$
$1384.173176$
1.945184808
\( \frac{35152}{9} \)
\( \bigl[a^{3} - 3 a\) , \( -1\) , \( a^{3} - 3 a\) , \( -2\) , \( 0\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}-{x}^{2}-2{x}$
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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.