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-c1
27.2-c
$2$
$3$
4.4.19821.1
$4$
$[4, 0]$
27.2
\( 3^{3} \)
\( 3^{3} \)
$18.99423$
$(-1/3a^3-1/3a^2+3a+2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$9$
\( 1 \)
$1$
$241.7504940$
1.717135589
\( \frac{18512}{3} a^{3} + \frac{1769}{3} a^{2} - 48583 a - 15892 \)
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 2\) , \( a\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} - a + 2\) , \( a^{3} - 3 a^{2} + 2 a\bigr] \)
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a-1\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+2a-2\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}-a+2\right){x}+a^{3}-3a^{2}+2a$
27.2-d2
27.2-d
$2$
$3$
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
$1$
\( 1 \)
$1$
$196.1860248$
1.393494589
\( \frac{18512}{3} a^{3} + \frac{1769}{3} a^{2} - 48583 a - 15892 \)
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( -a^{2} + 5\) , \( a\) , \( -a^{2} - a + 9\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - 2 a + 5\bigr] \)
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-2a\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-a^{2}-a+9\right){x}+\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-2a+5$
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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.