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-c2
27.1-c
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
27.1
\( 3^{3} \)
\( 3^{11} \)
$31.83578$
$(-a^4+a^3+4a^2-2a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.070190700$
$1906.865301$
2.61173484
\( -1283318 a^{4} + 1637833 a^{3} + 6106189 a^{2} - 4095058 a - 5583206 \)
\( \bigl[a^{2} - 2\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 5 a - 5\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( -3 a^{4} + 2 a^{3} + 13 a^{2} - a - 3\) , \( -18 a^{4} - 5 a^{3} + 80 a^{2} + 68 a + 10\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(-a^{4}+a^{3}+5a^{2}-3a-4\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-5a-5\right){x}^{2}+\left(-3a^{4}+2a^{3}+13a^{2}-a-3\right){x}-18a^{4}-5a^{3}+80a^{2}+68a+10$
27.1-d2
27.1-d
$2$
$3$
5.5.65657.1
$5$
$[5, 0]$
27.1
\( 3^{3} \)
\( 3^{5} \)
$31.83578$
$(-a^4+a^3+4a^2-2a-2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$2978.683972$
1.29163975
\( -1283318 a^{4} + 1637833 a^{3} + 6106189 a^{2} - 4095058 a - 5583206 \)
\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( a^{2} - a - 2\) , \( -2 a^{2} + 3 a + 4\) , \( -2 a^{4} - 2 a^{3} + 10 a^{2} + 12 a + 3\bigr] \)
${y}^2+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}^{2}+\left(-2a^{2}+3a+4\right){x}-2a^{4}-2a^{3}+10a^{2}+12a+3$
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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.