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
84.1-a1
84.1-a
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
84.1
\( 2^{2} \cdot 3 \cdot 7 \)
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \)
$1.23970$
$(-a+2), (a+3), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{6} \)
$1$
$2.486887276$
2.170733179
\( -\frac{7189057}{16128} \)
\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 22 a - 52\) , \( 166 a - 457\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22a-52\right){x}+166a-457$
84.1-b1
84.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
84.1
\( 2^{2} \cdot 3 \cdot 7 \)
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \)
$1.23970$
$(-a+2), (a+3), (2)$
$1$
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{5} \)
$0.553231005$
$12.07873502$
1.458204113
\( -\frac{7189057}{16128} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$
252.1-b1
252.1-b
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
252.1
\( 2^{2} \cdot 3^{2} \cdot 7 \)
\( 2^{16} \cdot 3^{10} \cdot 7^{2} \)
$1.63154$
$(-a+2), (a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.164303633$
1.381015326
\( -\frac{7189057}{16128} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 16 a - 29\) , \( -83 a + 237\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(16a-29\right){x}-83a+237$
252.1-c1
252.1-c
$6$
$8$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
252.1
\( 2^{2} \cdot 3^{2} \cdot 7 \)
\( 2^{16} \cdot 3^{10} \cdot 7^{2} \)
$1.63154$
$(-a+2), (a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.164303633$
1.381015326
\( -\frac{7189057}{16128} \)
\( \bigl[a\) , \( a\) , \( 1\) , \( -11 a - 21\) , \( 63 a + 110\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-11a-21\right){x}+63a+110$
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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.