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
6669.1-a1
6669.1-a
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
6669.1
\( 3^{3} \cdot 13 \cdot 19 \)
\( 3^{5} \cdot 13^{5} \cdot 19^{2} \)
$1.39867$
$(-2a+1), (-4a+1), (-5a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \cdot 3 \cdot 5 \)
$0.013301907$
$1.783431706$
1.643580646
\( -\frac{4423683938}{134036773} a + \frac{396021612979}{134036773} \)
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -20 a + 6\) , \( 14 a - 20\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a+6\right){x}+14a-20$
6669.1-b1
6669.1-b
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
6669.1
\( 3^{3} \cdot 13 \cdot 19 \)
\( 3^{3} \cdot 13 \cdot 19^{2} \)
$1.39867$
$(-2a+1), (-4a+1), (-5a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$0.083724838$
$5.074069545$
1.962185644
\( \frac{4943463}{4693} a - \frac{6976821}{4693} \)
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -a + 2\) , \( -2 a + 1\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+2\right){x}-2a+1$
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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.