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
32.1-a1
32.1-a
$4$
$4$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{12} \)
$1.99373$
$(-3a-14)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$2$
2Cs
$1$
\( 2 \)
$4.253144970$
$27.50074327$
3.117118340
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
${y}^2={x}^{3}-{x}$
32.1-a2
32.1-a
$4$
$4$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{12} \)
$1.99373$
$(-3a-14)$
$1$
$\Z/4\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$8.506289940$
$13.75037163$
3.117118340
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16548 a + 77617\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(16548a+77617\right){x}$
32.1-a3
32.1-a
$4$
$4$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{6} \)
$1.99373$
$(-3a-14)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$2.126572485$
$13.75037163$
3.117118340
\( 287496 \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -45507 a - 213451\) , \( -11478033 a - 53836749\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-45507a-213451\right){x}-11478033a-53836749$
32.1-a4
32.1-a
$4$
$4$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{6} \)
$1.99373$
$(-3a-14)$
$1$
$\Z/4\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$2.126572485$
$55.00148654$
3.117118340
\( 287496 \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -45507 a - 213440\) , \( 11341512 a + 53196410\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-45507a-213440\right){x}+11341512a+53196410$
32.1-b1
32.1-b
$4$
$4$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{12} \)
$1.99373$
$(-3a-14)$
0
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$1$
$13.75037163$
0.732897270
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2={x}^{3}+{x}$
32.1-b2
32.1-b
$4$
$4$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{12} \)
$1.99373$
$(-3a-14)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$27.50074327$
0.732897270
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16548 a - 77617\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-16548a-77617\right){x}$
32.1-b3
32.1-b
$4$
$4$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{6} \)
$1.99373$
$(-3a-14)$
0
$\Z/2\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$1$
$13.75037163$
0.732897270
\( 287496 \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -7\) , \( -8\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-7{x}-8$
32.1-b4
32.1-b
$4$
$4$
\(\Q(\sqrt{22}) \)
$2$
$[2, 0]$
32.1
\( 2^{5} \)
\( 2^{6} \)
$1.99373$
$(-3a-14)$
0
$\Z/4\Z$
$\textsf{potential}$
$-16$
$N(\mathrm{U}(1))$
✓
✓
✓
$1$
\( 2 \)
$1$
$55.00148654$
0.732897270
\( 287496 \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( 1\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+4{x}+1$
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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.