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
576.4-b1
576.4-b
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.4
\( 2^{6} \cdot 3^{2} \)
\( 2^{21} \cdot 3^{4} \)
$1.80496$
$(-a+2), (-a-1), (3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \cdot 3 \)
$1$
$3.901944618$
2.839081730
\( \frac{10977761}{36864} a + \frac{4203325}{9216} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( 6 a + 8\) , \( -7 a - 12\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(6a+8\right){x}-7a-12$
576.4-g1
576.4-g
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
576.4
\( 2^{6} \cdot 3^{2} \)
\( 2^{21} \cdot 3^{4} \)
$1.80496$
$(-a+2), (-a-1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.623239064$
$7.226387926$
2.184648010
\( \frac{10977761}{36864} a + \frac{4203325}{9216} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 8\) , \( -60 a + 152\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-8\right){x}-60a+152$
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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.