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
22.1-a1 22.1-a $4$
$4$
3.3.316.1 $3$
$[3, 0]$
22.1
\( 2 \cdot 11 \)
\( - 2^{7} \cdot 11 \)
$2.65901$
$(-a+1), (a^2-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$70.51182219$
0.991649975
\( \frac{7492235415}{1408} a^{2} + \frac{4985176571}{704} a - \frac{3177054421}{704} \)
\( \bigl[a^{2} + a - 3\) , \( a^{2} + a - 4\) , \( 1\) , \( 12 a^{2} - 38\) , \( 33 a^{2} - 10 a - 127\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(12a^{2}-38\right){x}+33a^{2}-10a-127$
22.1-a2 22.1-a $4$
$4$
3.3.316.1 $3$
$[3, 0]$
22.1
\( 2 \cdot 11 \)
\( - 2^{28} \cdot 11 \)
$2.65901$
$(-a+1), (a^2-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$35.25591109$
0.991649975
\( \frac{2181946399403}{2952790016} a^{2} + \frac{2000899833535}{1476395008} a + \frac{2482359162991}{1476395008} \)
\( \bigl[1\) , \( a^{2} - a - 2\) , \( 1\) , \( 177 a^{2} - 284 a - 1094\) , \( 821 a^{2} - 2362 a - 6983\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(177a^{2}-284a-1094\right){x}+821a^{2}-2362a-6983$
22.1-a3 22.1-a $4$
$4$
3.3.316.1 $3$
$[3, 0]$
22.1
\( 2 \cdot 11 \)
\( - 2^{7} \cdot 11^{4} \)
$2.65901$
$(-a+1), (a^2-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$17.62795554$
0.991649975
\( -\frac{2929687672739594901}{1874048} a^{2} + \frac{775365998006910655}{937024} a + \frac{6224327636401209327}{937024} \)
\( \bigl[1\) , \( a - 1\) , \( a\) , \( 3 a^{2} + 37 a - 20\) , \( 128 a^{2} + 21 a - 39\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a^{2}+37a-20\right){x}+128a^{2}+21a-39$
22.1-a4 22.1-a $4$
$4$
3.3.316.1 $3$
$[3, 0]$
22.1
\( 2 \cdot 11 \)
\( 2^{14} \cdot 11^{2} \)
$2.65901$
$(-a+1), (a^2-a-1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{2} \)
$1$
$70.51182219$
0.991649975
\( -\frac{1196719965343}{1982464} a^{2} + \frac{318008627741}{991232} a + \frac{2546638361901}{991232} \)
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -7 a^{2} - 8 a + 5\) , \( 13 a^{2} + 15 a - 10\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a^{2}-8a+5\right){x}+13a^{2}+15a-10$
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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.
