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
47.2-a2 47.2-a $4$
$4$
\(\Q(\sqrt{2}, \sqrt{3})\) $4$
$[4, 0]$
47.2
\( 47 \)
\( 47^{2} \)
$6.94052$
$(a^3+2a^2-2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2 \)
$1$
$840.2445428$
2.188136830
\( \frac{27756544}{2209} a^{3} + \frac{44907520}{2209} a^{2} - \frac{20659712}{2209} a - \frac{948672}{2209} \)
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a\) , \( -2 a^{3} + 2 a^{2} + 3 a\) , \( -a^{3} + a^{2} + 2 a - 1\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+a{y}={x}^{3}+\left(a^{3}+a^{2}-5a-1\right){x}^{2}+\left(-2a^{3}+2a^{2}+3a\right){x}-a^{3}+a^{2}+2a-1$
47.2-b2 47.2-b $4$
$4$
\(\Q(\sqrt{2}, \sqrt{3})\) $4$
$[4, 0]$
47.2
\( 47 \)
\( 47^{2} \)
$6.94052$
$(a^3+2a^2-2)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2 \)
$0.042934880$
$2021.407957$
0.904051146
\( \frac{27756544}{2209} a^{3} + \frac{44907520}{2209} a^{2} - \frac{20659712}{2209} a - \frac{948672}{2209} \)
\( \bigl[a^{2} - 1\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{3} - 4 a\) , \( 3 a^{3} + a^{2} - 7 a + 1\) , \( a^{3} + a^{2} - a - 1\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(3a^{3}+a^{2}-7a+1\right){x}+a^{3}+a^{2}-a-1$
Download
displayed columns for
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.
