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
2268.1-h3
2268.1-h
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2268.1
\( 2^{2} \cdot 3^{4} \cdot 7 \)
\( 2^{18} \cdot 3^{6} \cdot 7^{2} \)
$2.82591$
$(-a+2), (a+3), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 2 \cdot 3^{2} \)
$0.179845539$
$3.511473982$
4.961145663
\( \frac{4492125}{3584} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -53 a + 147\) , \( 126 a - 352\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-53a+147\right){x}+126a-352$
2268.1-k3
2268.1-k
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2268.1
\( 2^{2} \cdot 3^{4} \cdot 7 \)
\( 2^{18} \cdot 3^{12} \cdot 7^{2} \)
$2.82591$
$(-a+2), (a+3), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$1$
$2.350635247$
1.025901328
\( \frac{4492125}{3584} \)
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 29 a + 62\) , \( 93 a + 172\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(29a+62\right){x}+93a+172$
2268.1-v3
2268.1-v
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2268.1
\( 2^{2} \cdot 3^{4} \cdot 7 \)
\( 2^{18} \cdot 3^{6} \cdot 7^{2} \)
$2.82591$
$(-a+2), (a+3), (2)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3^{3} \)
$0.424276273$
$4.720655279$
5.244723915
\( \frac{4492125}{3584} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 10\) , \( 5\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+10{x}+5$
2268.1-x3
2268.1-x
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2268.1
\( 2^{2} \cdot 3^{4} \cdot 7 \)
\( 2^{18} \cdot 3^{12} \cdot 7^{2} \)
$2.82591$
$(-a+2), (a+3), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$1$
$2.350635247$
1.025901328
\( \frac{4492125}{3584} \)
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -31 a + 92\) , \( -94 a + 266\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-31a+92\right){x}-94a+266$
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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.