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-e6
192.1-e
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
192.1
\( 2^{6} \cdot 3 \)
\( 2^{22} \cdot 3^{4} \)
$1.52431$
$(-a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$11.36701703$
2.480486475
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1922 a - 5379\) , \( -68449 a + 191102\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(1922a-5379\right){x}-68449a+191102$
192.1-j6
192.1-j
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
192.1
\( 2^{6} \cdot 3 \)
\( 2^{22} \cdot 3^{4} \)
$1.52431$
$(-a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$6.551017245$
$1.162639934$
1.662050944
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \)
${y}^2={x}^{3}-{x}^{2}-384{x}-2772$
576.1-c6
576.1-c
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{10} \)
$2.00611$
$(-a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$7.063080417$
$2.098868579$
3.234966217
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1154 a - 3457\) , \( 34417 a - 94933\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(1154a-3457\right){x}+34417a-94933$
576.1-k6
576.1-k
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{10} \)
$2.00611$
$(-a+2), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$7.063080417$
$2.098868579$
3.234966217
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1152 a - 2304\) , \( -33264 a - 58212\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1152a-2304\right){x}-33264a-58212$
768.1-q6
768.1-q
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
768.1
\( 2^{8} \cdot 3 \)
\( 2^{22} \cdot 3^{4} \)
$2.15570$
$(-a+2), (2)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.645289777$
$11.36701703$
3.201265131
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -384\) , \( 2772\bigr] \)
${y}^2={x}^{3}+{x}^{2}-384{x}+2772$
768.1-bi6
768.1-bi
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
768.1
\( 2^{8} \cdot 3 \)
\( 2^{22} \cdot 3^{4} \)
$2.15570$
$(-a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2^{3} \)
$1$
$1.162639934$
2.029670668
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 1922 a - 5379\) , \( 68449 a - 191102\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(1922a-5379\right){x}+68449a-191102$
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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.