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
20577.3-a1 20577.3-a $1$
$1$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
20577.3
\( 3 \cdot 19^{3} \)
\( 3^{6} \cdot 19^{4} \)
$1.85372$
$(-2a+1), (-5a+3), (-5a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2^{2} \cdot 3 \)
$0.041525978$
$2.801828385$
3.224348781
\( -\frac{1024000}{513} a - \frac{512000}{171} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 5 a - 8\) , \( -7 a + 6\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(5a-8\right){x}-7a+6$
61731.3-e1 61731.3-e $1$
$1$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
61731.3
\( 3^{2} \cdot 19^{3} \)
\( 3^{12} \cdot 19^{10} \)
$2.43964$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2^{2} \)
$1$
$0.371111235$
1.714089374
\( -\frac{1024000}{513} a - \frac{512000}{171} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 366 a - 450\) , \( -4386 a + 3212\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(366a-450\right){x}-4386a+3212$
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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.
