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
218.2-a1
218.2-a
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
218.2
\( 2 \cdot 109 \)
\( 2^{27} \cdot 109 \)
$0.90845$
$(a), (4a-11)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$0.846068882$
0.639567958
\( -\frac{93241301714587169}{14629732352} a - \frac{523000657128544837}{14629732352} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 179 a - 350\) , \( 1720 a - 1930\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(179a-350\right){x}+1720a-1930$
218.2-a2
218.2-a
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
218.2
\( 2 \cdot 109 \)
\( 2^{3} \cdot 109 \)
$0.90845$
$(a), (4a-11)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$7.614619944$
0.639567958
\( \frac{657631}{872} a - \frac{1623877}{872} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}-a{x}$
218.2-a3
218.2-a
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
218.2
\( 2 \cdot 109 \)
\( 2^{9} \cdot 109^{3} \)
$0.90845$
$(a), (4a-11)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 3 \)
$1$
$2.538206648$
0.639567958
\( -\frac{175486627225}{663054848} a + \frac{757473957219}{663054848} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 4 a - 5\) , \( -a - 4\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4a-5\right){x}-a-4$
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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.