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
27.2-c2
27.2-c
$2$
$3$
4.4.19821.1
$4$
$[4, 0]$
27.2
\( 3^{3} \)
\( 3^{9} \)
$18.99423$
$(-1/3a^3-1/3a^2+3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$81$
\( 1 \)
$1$
$2.984574000$
1.717135589
\( \frac{69390538551526}{3} a^{3} + \frac{7310207971123}{3} a^{2} - 182347992864521 a - 62777053162061 \)
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 2\) , \( a\) , \( 18 a^{3} - 65 a^{2} + 34 a + 12\) , \( \frac{701}{3} a^{3} - \frac{2560}{3} a^{2} + 416 a + 253\bigr] \)
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-2\right){x}^{2}+\left(18a^{3}-65a^{2}+34a+12\right){x}+\frac{701}{3}a^{3}-\frac{2560}{3}a^{2}+416a+253$
27.2-d1
27.2-d
$2$
$3$
4.4.19821.1
$4$
$[4, 0]$
27.2
\( 3^{3} \)
\( 3^{3} \)
$18.99423$
$(-1/3a^3-1/3a^2+3a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$9$
\( 1 \)
$1$
$21.79844721$
1.393494589
\( \frac{69390538551526}{3} a^{3} + \frac{7310207971123}{3} a^{2} - 182347992864521 a - 62777053162061 \)
\( \bigl[a^{2} - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( \frac{19}{3} a^{3} + \frac{1}{3} a^{2} - 63 a - 29\) , \( 7 a^{3} - 18 a^{2} - 128 a - 55\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-3a-1\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-4a-2\right){x}^{2}+\left(\frac{19}{3}a^{3}+\frac{1}{3}a^{2}-63a-29\right){x}+7a^{3}-18a^{2}-128a-55$
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Pari/GP
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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.