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
336.1-a2
336.1-a
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
336.1
\( 2^{4} \cdot 3 \cdot 7 \)
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \)
$1.75321$
$(-a+2), (a+3), (2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \cdot 3^{2} \)
$1$
$4.797489038$
2.093795872
\( \frac{2048000}{1323} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 7\) , \( 0\bigr] \)
${y}^2={x}^{3}+{x}^{2}+7{x}$
336.1-d2
336.1-d
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
336.1
\( 2^{4} \cdot 3 \cdot 7 \)
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \)
$1.75321$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \cdot 3 \)
$0.166492135$
$5.711517702$
2.490100344
\( \frac{2048000}{1323} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -33 a + 95\) , \( -34 a + 96\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-33a+95\right){x}-34a+96$
1008.1-b2
1008.1-b
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1008.1
\( 2^{4} \cdot 3^{2} \cdot 7 \)
\( 2^{8} \cdot 3^{12} \cdot 7^{4} \)
$2.30735$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$2.673064348$
$3.022192558$
3.525753077
\( \frac{2048000}{1323} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -19 a + 62\) , \( 20 a - 62\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-19a+62\right){x}+20a-62$
1008.1-c2
1008.1-c
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1008.1
\( 2^{4} \cdot 3^{2} \cdot 7 \)
\( 2^{8} \cdot 3^{12} \cdot 7^{4} \)
$2.30735$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$2.673064348$
$3.022192558$
3.525753077
\( \frac{2048000}{1323} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 21 a + 42\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(21a+42\right){x}$
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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.