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
2178.5-a2
2178.5-a
$8$
$12$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
2178.5
\( 2 \cdot 3^{2} \cdot 11^{2} \)
\( 2^{2} \cdot 3^{12} \cdot 11^{4} \)
$1.72662$
$(a), (-a-1), (a-1), (a+3), (a-3)$
$1$
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{5} \cdot 3^{2} \)
$0.516109614$
$1.869402865$
2.728913986
\( \frac{9938375}{176418} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+4{x}+20$
17424.5-e2
17424.5-e
$8$
$12$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
17424.5
\( 2^{4} \cdot 3^{2} \cdot 11^{2} \)
\( 2^{14} \cdot 3^{12} \cdot 11^{4} \)
$2.90383$
$(a), (-a-1), (a-1), (a+3), (a-3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3B
$1$
\( 2^{6} \)
$0.550897322$
$0.934701432$
2.912852940
\( \frac{9938375}{176418} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 18\) , \( 162\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+18{x}+162$
19602.8-g2
19602.8-g
$8$
$12$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
19602.8
\( 2 \cdot 3^{4} \cdot 11^{2} \)
\( 2^{2} \cdot 3^{24} \cdot 11^{4} \)
$2.99060$
$(a), (-a-1), (a-1), (a+3), (a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2Cs , 3B.1.2
$1$
\( 2^{7} \)
$1$
$0.623134288$
3.524979847
\( \frac{9938375}{176418} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( -547\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+40{x}-547$
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Pari/GP
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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.