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-a5
21.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{4} \cdot 7^{8} \)
$0.87660$
$(-a+2), (a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$14.60752776$
0.796905972
\( \frac{13027640977}{21609} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 245 a - 687\) , \( -3019 a + 8425\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(245a-687\right){x}-3019a+8425$
21.1-b5
21.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
21.1
\( 3 \cdot 7 \)
\( 3^{4} \cdot 7^{8} \)
$0.87660$
$(-a+2), (a+3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1.319254411$
$3.256081743$
0.937376813
\( \frac{13027640977}{21609} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \)
${y}^2+{x}{y}={x}^{3}-49{x}-136$
63.1-a5
63.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
63.1
\( 3^{2} \cdot 7 \)
\( 3^{10} \cdot 7^{8} \)
$1.15367$
$(-a+2), (a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$3.981762779$
1.737783746
\( \frac{13027640977}{21609} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 147 a - 441\) , \( 1632 a - 4488\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(147a-441\right){x}+1632a-4488$
63.1-b5
63.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
63.1
\( 3^{2} \cdot 7 \)
\( 3^{10} \cdot 7^{8} \)
$1.15367$
$(-a+2), (a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$3.981762779$
1.737783746
\( \frac{13027640977}{21609} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -147 a - 294\) , \( -1632 a - 2856\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-147a-294\right){x}-1632a-2856$
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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.