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
14.2-a1
14.2-a
$4$
$27$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
14.2
\( 2 \cdot 7 \)
\( 2^{18} \cdot 7^{9} \)
$0.96239$
$(2,a), (7,a+4)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3^{2} \)
$1$
$1.122170831$
0.806191324
\( -\frac{3429643149944533}{10578455953408} a - \frac{436912252725523}{10578455953408} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a + 29\) , \( -24 a - 42\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a+29\right){x}-24a-42$
14.2-a2
14.2-a
$4$
$27$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
14.2
\( 2 \cdot 7 \)
\( 2^{54} \cdot 7^{3} \)
$0.96239$
$(2,a), (7,a+4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 2 \cdot 3 \)
$1$
$0.374056943$
0.806191324
\( \frac{1524255431343666912883}{6178938688752320512} a + \frac{1865190650273146662373}{6178938688752320512} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a - 266\) , \( 467 a + 1516\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(4a-266\right){x}+467a+1516$
14.2-a3
14.2-a
$4$
$27$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
14.2
\( 2 \cdot 7 \)
\( 2^{2} \cdot 7 \)
$0.96239$
$(2,a), (7,a+4)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 2 \)
$1$
$10.09953748$
0.806191324
\( \frac{17387}{28} a + \frac{61997}{28} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}$
14.2-a4
14.2-a
$4$
$27$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
14.2
\( 2 \cdot 7 \)
\( 2^{6} \cdot 7^{3} \)
$0.96239$
$(2,a), (7,a+4)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1$
$3.366512495$
0.806191324
\( -\frac{25508811437}{21952} a + \frac{14931496453}{21952} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( -a - 38\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(4a+4\right){x}-a-38$
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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.