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
28.1-a2
28.1-a
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{4} \cdot 7^{2} \)
$0.94197$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$1$
$7.027708105$
1.533571636
\( -\frac{15625}{28} \)
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 2 a - 8\) , \( 8 a - 25\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a-8\right){x}+8a-25$
28.1-b2
28.1-b
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
28.1
\( 2^{2} \cdot 7 \)
\( 2^{4} \cdot 7^{2} \)
$0.94197$
$(a+3), (2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$1$
$35.33144352$
0.856661451
\( -\frac{15625}{28} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}$
252.1-a2
252.1-a
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
252.1
\( 2^{2} \cdot 3^{2} \cdot 7 \)
\( 2^{4} \cdot 3^{6} \cdot 7^{2} \)
$1.63154$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.293017631$
$9.097601735$
2.326864094
\( -\frac{15625}{28} \)
\( \bigl[a\) , \( -1\) , \( 1\) , \( -2 a - 3\) , \( 3 a + 5\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2a-3\right){x}+3a+5$
252.1-d2
252.1-d
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
252.1
\( 2^{2} \cdot 3^{2} \cdot 7 \)
\( 2^{4} \cdot 3^{6} \cdot 7^{2} \)
$1.63154$
$(-a+2), (a+3), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.293017631$
$9.097601735$
2.326864094
\( -\frac{15625}{28} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( a - 5\) , \( -3 a + 8\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-5\right){x}-3a+8$
1792.1-d2
1792.1-d
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{28} \cdot 7^{2} \)
$2.66430$
$(a+3), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$4$
\( 2^{3} \)
$1$
$1.756927026$
3.067143272
\( -\frac{15625}{28} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -8\) , \( -16\bigr] \)
${y}^2={x}^{3}-{x}^{2}-8{x}-16$
1792.1-bp2
1792.1-bp
$6$
$18$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{28} \cdot 7^{2} \)
$2.66430$
$(a+3), (2)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.273389205$
$8.832860880$
4.215635879
\( -\frac{15625}{28} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 42 a - 115\) , \( -425 a + 1186\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(42a-115\right){x}-425a+1186$
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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.