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
3249.3-a1
3249.3-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3249.3
\( 3^{2} \cdot 19^{2} \)
\( 3^{3} \cdot 19^{9} \)
$1.16852$
$(-2a+1), (-5a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{2} \)
$1$
$1.078091533$
1.244872874
\( -\frac{29840721}{6859} a - \frac{5426511}{6859} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 17 a + 39\) , \( 156 a - 114\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(17a+39\right){x}+156a-114$
3249.3-a2
3249.3-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3249.3
\( 3^{2} \cdot 19^{2} \)
\( 3^{3} \cdot 19^{12} \)
$1.16852$
$(-2a+1), (-5a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{3} \)
$1$
$0.539045766$
1.244872874
\( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -168 a + 94\) , \( 544 a - 1166\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-168a+94\right){x}+544a-1166$
3249.3-a3
3249.3-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3249.3
\( 3^{2} \cdot 19^{2} \)
\( 3^{9} \cdot 19^{7} \)
$1.16852$
$(-2a+1), (-5a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{2} \)
$1$
$1.078091533$
1.244872874
\( \frac{9153}{19} a + \frac{27648}{19} \)
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -37 a + 44\) , \( 47 a + 15\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-37a+44\right){x}+47a+15$
3249.3-a4
3249.3-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3249.3
\( 3^{2} \cdot 19^{2} \)
\( 3^{9} \cdot 19^{8} \)
$1.16852$
$(-2a+1), (-5a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{3} \)
$1$
$0.539045766$
1.244872874
\( \frac{363527109}{361} a - \frac{76135923}{361} \)
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -427 a + 599\) , \( 2309 a + 3294\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-427a+599\right){x}+2309a+3294$
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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.