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
27.1-a3
27.1-a
$3$
$9$
4.4.9909.1
$4$
$[4, 0]$
27.1
\( 3^{3} \)
\( 3^{3} \)
$13.42994$
$(-a^3+a^2+4a)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 1 \)
$0.961672007$
$684.6007343$
2.939455590
\( -19062 a^{3} - 54036 a^{2} - 17262 a + 24435 \)
\( \bigl[a\) , \( 0\) , \( a^{2} - 2\) , \( 2 a^{3} - 3 a^{2} - 10 a + 6\) , \( 17 a^{3} - 21 a^{2} - 78 a + 42\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(2a^{3}-3a^{2}-10a+6\right){x}+17a^{3}-21a^{2}-78a+42$
27.1-g2
27.1-g
$3$
$9$
4.4.9909.1
$4$
$[4, 0]$
27.1
\( 3^{3} \)
\( 3^{3} \)
$13.42994$
$(-a^3+a^2+4a)$
$0 \le r \le 1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
\( 1 \)
$1$
$292.2932950$
2.869118658
\( -19062 a^{3} - 54036 a^{2} - 17262 a + 24435 \)
\( \bigl[a^{3} - 5 a - 2\) , \( a - 1\) , \( a + 1\) , \( -2 a^{2} + 10\) , \( -9 a^{3} + 10 a^{2} + 41 a - 20\bigr] \)
${y}^2+\left(a^{3}-5a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a^{2}+10\right){x}-9a^{3}+10a^{2}+41a-20$
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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.