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-h1
2268.1-h
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2268.1
\( 2^{2} \cdot 3^{4} \cdot 7 \)
\( 2^{2} \cdot 3^{10} \cdot 7^{2} \)
$2.82591$
$(-a+2), (a+3), (2)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3 \)
$1.618609852$
$10.53442194$
4.961145663
\( -\frac{545407363875}{14} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1062\) , \( 13590\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-1062{x}+13590$
2268.1-k1
2268.1-k
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2268.1
\( 2^{2} \cdot 3^{4} \cdot 7 \)
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \)
$2.82591$
$(-a+2), (a+3), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$1$
$2.350635247$
1.025901328
\( -\frac{545407363875}{14} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -354 a - 708\) , \( -6040 a - 10570\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-354a-708\right){x}-6040a-10570$
2268.1-v1
2268.1-v
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2268.1
\( 2^{2} \cdot 3^{4} \cdot 7 \)
\( 2^{2} \cdot 3^{10} \cdot 7^{2} \)
$2.82591$
$(-a+2), (a+3), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$9$
\( 2 \)
$3.818486457$
$0.174839084$
5.244723915
\( -\frac{545407363875}{14} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 5310 a - 14868\) , \( 326160 a - 910530\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5310a-14868\right){x}+326160a-910530$
2268.1-x1
2268.1-x
$3$
$9$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
2268.1
\( 2^{2} \cdot 3^{4} \cdot 7 \)
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \)
$2.82591$
$(-a+2), (a+3), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2 \)
$1$
$2.350635247$
1.025901328
\( -\frac{545407363875}{14} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 354 a - 1062\) , \( 6040 a - 16610\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(354a-1062\right){x}+6040a-16610$
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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.