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
21.1-a1
21.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{2} \cdot 7^{16} \)
$0.87660$
$(-a+2), (a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$3.651881942$
0.796905972
\( -\frac{4354703137}{17294403} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 170 a - 477\) , \( -5038 a + 14062\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(170a-477\right){x}-5038a+14062$
21.1-b1
21.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{2} \cdot 7^{16} \)
$0.87660$
$(-a+2), (a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$2.638508823$
$0.814020435$
0.937376813
\( -\frac{4354703137}{17294403} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \)
${y}^2+{x}{y}={x}^{3}-34{x}-217$
63.1-a1
63.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
63.1
\( 3^{2} \cdot 7 \)
\( 3^{8} \cdot 7^{16} \)
$1.15367$
$(-a+2), (a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$0.995440694$
1.737783746
\( -\frac{4354703137}{17294403} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 102 a - 306\) , \( 2604 a - 7161\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(102a-306\right){x}+2604a-7161$
63.1-b1
63.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
63.1
\( 3^{2} \cdot 7 \)
\( 3^{8} \cdot 7^{16} \)
$1.15367$
$(-a+2), (a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$0.995440694$
1.737783746
\( -\frac{4354703137}{17294403} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -102 a - 204\) , \( -2604 a - 4557\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-102a-204\right){x}-2604a-4557$
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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.