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-c1
27.1-c
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
27.1
\( 3^{3} \)
\( 3^{9} \)
$31.83578$
$(-a^4+a^3+4a^2-2a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.210572102$
$635.6217671$
2.61173484
\( -24302019083166184075 a^{4} + 29987786156907253441 a^{3} + 114494070674765766206 a^{2} - 75391385133403896914 a - 103871320062709432359 \)
\( \bigl[a^{2} - a - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 7\) , \( a + 1\) , \( 6 a^{4} - 15 a^{3} - 24 a^{2} + 36 a + 16\) , \( 18 a^{4} - 27 a^{3} - 60 a^{2} + 70 a + 21\bigr] \)
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2a^{4}-2a^{3}-9a^{2}+4a+7\right){x}^{2}+\left(6a^{4}-15a^{3}-24a^{2}+36a+16\right){x}+18a^{4}-27a^{3}-60a^{2}+70a+21$
27.1-d1
27.1-d
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
27.1
\( 3^{3} \)
\( 3^{3} \)
$31.83578$
$(-a^4+a^3+4a^2-2a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$9$
\( 1 \)
$1$
$36.77387620$
1.29163975
\( -24302019083166184075 a^{4} + 29987786156907253441 a^{3} + 114494070674765766206 a^{2} - 75391385133403896914 a - 103871320062709432359 \)
\( \bigl[a^{2} - 2\) , \( -a^{4} + 5 a^{2} - 2\) , \( a^{2} - a - 1\) , \( 3 a^{4} - 9 a^{3} - 7 a^{2} + 21 a + 2\) , \( 9 a^{4} - 15 a^{3} - 40 a^{2} + 52 a + 13\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-2\right){x}^{2}+\left(3a^{4}-9a^{3}-7a^{2}+21a+2\right){x}+9a^{4}-15a^{3}-40a^{2}+52a+13$
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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.