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
576.1-e6
576.1-e
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{4} \)
$0.97888$
$(2), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2 \)
$1$
$1.162639934$
1.039896770
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \)
${y}^2={x}^{3}-{x}^{2}-384{x}-2772$
2304.1-b6
2304.1-b
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2304.1
\( 2^{8} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{4} \)
$1.38434$
$(2), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$3.635347017$
1.625776610
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 384 \phi - 768\) , \( -5544 \phi + 8316\bigr] \)
${y}^2={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(384\phi-768\right){x}-5544\phi+8316$
2304.1-m6
2304.1-m
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2304.1
\( 2^{8} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{4} \)
$1.38434$
$(2), (3)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.374241721$
$11.36701703$
1.902452012
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -384\) , \( 2772\bigr] \)
${y}^2={x}^{3}+{x}^{2}-384{x}+2772$
2304.1-p6
2304.1-p
$6$
$8$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
2304.1
\( 2^{8} \cdot 3^{2} \)
\( 2^{22} \cdot 3^{4} \)
$1.38434$
$(2), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$3.635347017$
1.625776610
\( \frac{3065617154}{9} \)
\( \bigl[0\) , \( \phi\) , \( 0\) , \( -384 \phi - 384\) , \( 5544 \phi + 2772\bigr] \)
${y}^2={x}^{3}+\phi{x}^{2}+\left(-384\phi-384\right){x}+5544\phi+2772$
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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.