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
27225.2-a1
27225.2-a
$2$
$2$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
27225.2
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)
\( 3^{9} \cdot 5^{9} \cdot 11^{3} \)
$3.80695$
$(-a), (-a-1), (a-2), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{5} \)
$0.502834080$
$0.750726747$
3.642170149
\( -\frac{24171483673}{390625} a - \frac{16292777334}{390625} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -120 a + 21\) , \( 584 a - 628\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-120a+21\right){x}+584a-628$
27225.2-e1
27225.2-e
$2$
$2$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
27225.2
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)
\( 3^{3} \cdot 5^{9} \cdot 11^{9} \)
$3.80695$
$(-a), (-a-1), (a-2), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{3} \)
$1$
$0.392054257$
1.891340900
\( -\frac{24171483673}{390625} a - \frac{16292777334}{390625} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -408 a + 493\) , \( -784 a + 7502\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-408a+493\right){x}-784a+7502$
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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.