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-a6
72.1-a
$10$
$32$
\(\Q(\sqrt{2}, \sqrt{3})\)
$4$
$[4, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{4} \)
$7.32059$
$(a^3-4a+1), (a^2-2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$4$
\( 2^{2} \)
$1$
$64.60453813$
1.345927877
\( \frac{28756228}{3} \)
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 4 a + 1\) , \( 17 a^{3} - 42 a^{2} + 13 a + 6\) , \( 135 a^{3} - 290 a^{2} + 33 a + 44\bigr] \)
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(17a^{3}-42a^{2}+13a+6\right){x}+135a^{3}-290a^{2}+33a+44$
72.1-b6
72.1-b
$10$
$32$
\(\Q(\sqrt{2}, \sqrt{3})\)
$4$
$[4, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{4} \cdot 3^{4} \)
$7.32059$
$(a^3-4a+1), (a^2-2)$
$1$
$\Z/2\Z\oplus\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$0.539636932$
$2768.346352$
1.945184808
\( \frac{28756228}{3} \)
\( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} - 1\) , \( 16 a^{3} - 40 a^{2} + 16 a + 1\) , \( -119 a^{3} + 249 a^{2} - 16 a - 42\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(16a^{3}-40a^{2}+16a+1\right){x}-119a^{3}+249a^{2}-16a-42$
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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.