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-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
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16548 a - 77617\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-16548a-77617\right){x}$
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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.
