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-e2 192.1-e $6$
$8$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
192.1
\( 2^{6} \cdot 3 \)
\( 2^{8} \cdot 3^{2} \)
$1.52431$
$(-a+2), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $4$
\( 2^{2} \)
$1$
$11.36701703$
2.480486475
\( \frac{2048}{3} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -3 a + 11\) , \( 4 a - 12\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-3a+11\right){x}+4a-12$
192.1-j2 192.1-j $6$
$8$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
192.1
\( 2^{6} \cdot 3 \)
\( 2^{8} \cdot 3^{2} \)
$1.52431$
$(-a+2), (2)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2^{2} \)
$0.818877155$
$18.60223895$
1.662050944
\( \frac{2048}{3} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}^{2}+{x}$
576.1-c2 576.1-c $6$
$8$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$2.00611$
$(-a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$0.882885052$
$8.395474317$
3.234966217
\( \frac{2048}{3} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a + 8\) , \( -2 a + 8\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-a+8\right){x}-2a+8$
576.1-k2 576.1-k $6$
$8$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$2.00611$
$(-a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$0.882885052$
$8.395474317$
3.234966217
\( \frac{2048}{3} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3 a + 6\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(3a+6\right){x}$
768.1-q2 768.1-q $6$
$8$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
768.1
\( 2^{8} \cdot 3 \)
\( 2^{8} \cdot 3^{2} \)
$2.15570$
$(-a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2 \)
$1.290579554$
$11.36701703$
3.201265131
\( \frac{2048}{3} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+{x}^{2}+{x}$
768.1-bi2 768.1-bi $6$
$8$
\(\Q(\sqrt{21}) \) $2$
$[2, 0]$
768.1
\( 2^{8} \cdot 3 \)
\( 2^{8} \cdot 3^{2} \)
$2.15570$
$(-a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2 \)
$1$
$18.60223895$
2.029670668
\( \frac{2048}{3} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -3 a + 11\) , \( -4 a + 12\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-3a+11\right){x}-4a+12$
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Pari/GP
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Magma
Oscar
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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.
