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
192.1-d1 192.1-d $4$
$4$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
192.1
\( 2^{6} \cdot 3 \)
\( - 2^{8} \cdot 3 \)
$1.52431$
$(-a+2), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 2 \)
$1$
$34.67048791$
0.945715090
\( -\frac{4864}{3} a + \frac{13568}{3} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 4 a + 7\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+{x}+4a+7$
192.1-k1 192.1-k $4$
$4$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
192.1
\( 2^{6} \cdot 3 \)
\( - 2^{8} \cdot 3 \)
$1.52431$
$(-a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 2 \)
$0.852762531$
$13.64169646$
2.538556564
\( -\frac{4864}{3} a + \frac{13568}{3} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+{x}$
576.1-j1 576.1-j $4$
$4$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( - 2^{8} \cdot 3^{7} \)
$2.00611$
$(-a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 2^{2} \)
$1$
$14.28756645$
3.117802608
\( -\frac{4864}{3} a + \frac{13568}{3} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 12\) , \( 9 a - 27\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-12\right){x}+9a-27$
576.1-m1 576.1-m $4$
$4$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( - 2^{8} \cdot 3^{7} \)
$2.00611$
$(-a+2), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 2^{3} \)
$1$
$11.03440239$
1.203952004
\( -\frac{4864}{3} a + \frac{13568}{3} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( -2 a - 3\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}-2a-3$
768.1-p1 768.1-p $4$
$4$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
768.1
\( 2^{8} \cdot 3 \)
\( - 2^{8} \cdot 3 \)
$2.15570$
$(-a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $4$
\( 1 \)
$1$
$13.64169646$
2.976862221
\( -\frac{4864}{3} a + \frac{13568}{3} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -4 a - 7\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+{x}-4a-7$
768.1-bg1 768.1-bg $4$
$4$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
768.1
\( 2^{8} \cdot 3 \)
\( - 2^{8} \cdot 3 \)
$2.15570$
$(-a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2B $1$
\( 1 \)
$0.864433776$
$34.67048791$
3.270032270
\( -\frac{4864}{3} a + \frac{13568}{3} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+{x}$
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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.
