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
5184.1-CMc1
5184.1-CMc
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
5184.1
\( 2^{6} \cdot 3^{4} \)
\( 2^{12} \cdot 3^{18} \)
$1.51647$
$(a+1), (3)$
0
$\Z/2\Z$
$\textsf{yes}$
$-4$
$\mathrm{U}(1)$
✓
✓
✓
$1$
\( 2^{3} \)
$1$
$1.323130127$
2.646260255
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \)
${y}^2={x}^{3}+27{x}$
5184.1-CMb1
5184.1-CMb
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
5184.1
\( 2^{6} \cdot 3^{4} \)
\( 2^{12} \cdot 3^{12} \)
$1.51647$
$(a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{yes}$
$-4$
$\mathrm{U}(1)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$2.291728606$
2.291728606
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \)
${y}^2={x}^{3}-9{x}$
5184.1-CMb2
5184.1-CMb
$2$
$2$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
5184.1
\( 2^{6} \cdot 3^{4} \)
\( 2^{6} \cdot 3^{12} \)
$1.51647$
$(a+1), (3)$
0
$\Z/2\Z$
$\textsf{yes}$
$-16$
$\mathrm{U}(1)$
✓
✓
✓
$1$
\( 2^{2} \)
$1$
$2.291728606$
2.291728606
\( 287496 \)
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 24\) , \( 59 i\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-i+24\right){x}+59i$
5184.1-CMa1
5184.1-CMa
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
5184.1
\( 2^{6} \cdot 3^{4} \)
\( 2^{12} \cdot 3^{6} \)
$1.51647$
$(a+1), (3)$
$2$
$\Z/2\Z$
$\textsf{yes}$
$-4$
$\mathrm{U}(1)$
✓
✓
✓
$1$
\( 2^{3} \)
$0.062795947$
$3.969390382$
1.994093041
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \)
${y}^2={x}^{3}+3{x}$
5184.1-a1
5184.1-a
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
5184.1
\( 2^{6} \cdot 3^{4} \)
\( 2^{6} \cdot 3^{20} \)
$1.51647$
$(a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.620169672$
$1.563576199$
1.939365079
\( \frac{97336}{81} \)
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -18\) , \( -27 i\bigr] \)
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}-18{x}-27i$
5184.1-a2
5184.1-a
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
5184.1
\( 2^{6} \cdot 3^{4} \)
\( 2^{12} \cdot 3^{16} \)
$1.51647$
$(a+1), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1.240339345$
$1.563576199$
1.939365079
\( \frac{21952}{9} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( 20\bigr] \)
${y}^2={x}^{3}-21{x}+20$
5184.1-a3
5184.1-a
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
5184.1
\( 2^{6} \cdot 3^{4} \)
\( 2^{12} \cdot 3^{14} \)
$1.51647$
$(a+1), (3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$0.620169672$
$1.563576199$
1.939365079
\( \frac{140608}{3} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 39\) , \( -92 i\bigr] \)
${y}^2={x}^{3}+39{x}-92i$
5184.1-a4
5184.1-a
$4$
$4$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
5184.1
\( 2^{6} \cdot 3^{4} \)
\( 2^{6} \cdot 3^{14} \)
$1.51647$
$(a+1), (3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$2.480678691$
$1.563576199$
1.939365079
\( \frac{7301384}{3} \)
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 72\) , \( 275 i\bigr] \)
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+72{x}+275i$
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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.