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
47.1-a1
47.1-a
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
47.1
\( 47 \)
\( -47 \)
$0.81050$
$(-4a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$19.40186574$
1.400209051
\( -\frac{51044}{47} a + \frac{29305}{47} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( a - 2\) , \( -1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a-2\right){x}-1$
47.1-a2
47.1-a
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
47.1
\( 47 \)
\( 47^{2} \)
$0.81050$
$(-4a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$9.700932874$
1.400209051
\( \frac{2284110745}{2209} a + \frac{4053285194}{2209} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 6 a - 12\) , \( 14 a - 25\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-12\right){x}+14a-25$
47.1-b1
47.1-b
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
47.1
\( 47 \)
\( -47 \)
$0.81050$
$(-4a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$0.098568841$
$39.61338472$
0.563587024
\( -\frac{51044}{47} a + \frac{29305}{47} \)
\( \bigl[1\) , \( a\) , \( 1\) , \( a - 1\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a-1\right){x}$
47.1-b2
47.1-b
$2$
$2$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
47.1
\( 47 \)
\( 47^{2} \)
$0.81050$
$(-4a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.049284420$
$39.61338472$
0.563587024
\( \frac{2284110745}{2209} a + \frac{4053285194}{2209} \)
\( \bigl[1\) , \( a\) , \( 1\) , \( 6 a - 11\) , \( -14 a + 24\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(6a-11\right){x}-14a+24$
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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.