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-c1
47.1-c
$2$
$2$
4.4.1957.1
$4$
$[4, 0]$
47.1
\( 47 \)
\( - 47^{2} \)
$6.39656$
$(2a^3-6a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.030350985$
$805.5519662$
1.105352853
\( \frac{260493073}{2209} a^{3} - \frac{513538831655}{2209} a^{2} + \frac{153993847068}{2209} a + \frac{1871080196928}{2209} \)
\( \bigl[a^{2} - a - 2\) , \( 2 a^{3} - a^{2} - 8 a + 1\) , \( -a^{3} + a^{2} + 3 a\) , \( -13 a^{3} + 8 a^{2} + 44 a - 21\) , \( 16 a^{3} - 14 a^{2} - 57 a + 29\bigr] \)
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{3}+a^{2}+3a\right){y}={x}^{3}+\left(2a^{3}-a^{2}-8a+1\right){x}^{2}+\left(-13a^{3}+8a^{2}+44a-21\right){x}+16a^{3}-14a^{2}-57a+29$
423.1-f2
423.1-f
$2$
$2$
4.4.1957.1
$4$
$[4, 0]$
423.1
\( 3^{2} \cdot 47 \)
\( - 3^{6} \cdot 47^{2} \)
$8.41834$
$(a^3-4a), (2a^3-6a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1$
$20.04749196$
1.812694539
\( \frac{260493073}{2209} a^{3} - \frac{513538831655}{2209} a^{2} + \frac{153993847068}{2209} a + \frac{1871080196928}{2209} \)
\( \bigl[-a^{3} + a^{2} + 3 a\) , \( 2 a^{3} - a^{2} - 8 a + 1\) , \( a\) , \( -62 a^{3} - 136 a^{2} - 32 a + 32\) , \( -824 a^{3} - 1705 a^{2} - 214 a + 401\bigr] \)
${y}^2+\left(-a^{3}+a^{2}+3a\right){x}{y}+a{y}={x}^{3}+\left(2a^{3}-a^{2}-8a+1\right){x}^{2}+\left(-62a^{3}-136a^{2}-32a+32\right){x}-824a^{3}-1705a^{2}-214a+401$
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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.