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
81.1-a1 81.1-a $4$
$27$
\(\Q(\sqrt{-183}) \) $2$
$[0, 1]$
81.1
\( 3^{4} \)
\( 3^{10} \)
$3.62648$
$(3,a+1)$
0
$\Z/3\Z$
$\textsf{potential}$
$-27$
$N(\mathrm{U}(1))$ ✓
✓
✓
$3$
3Cs.1.1 $9$
\( 1 \)
$1$
$2.702876088$
0.399604699
\( -12288000 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \) ${y}^2+{y}={x}^3-30{x}+63$
81.1-a2 81.1-a $4$
$27$
\(\Q(\sqrt{-183}) \) $2$
$[0, 1]$
81.1
\( 3^{4} \)
\( 3^{22} \)
$3.62648$
$(3,a+1)$
0
$\mathsf{trivial}$
$\textsf{potential}$
$-27$
$N(\mathrm{U}(1))$ ✓
✓
✓
$3$
3Cs.1.1 $1$
\( 1 \)
$1$
$2.702876088$
0.399604699
\( -12288000 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -270\) , \( -1708\bigr] \) ${y}^2+{y}={x}^3-270{x}-1708$
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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.
