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
36.4-a1
36.4-a
$4$
$6$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
36.4
\( 2^{2} \cdot 3^{2} \)
\( 2^{24} \cdot 3^{9} \)
$1.04973$
$(2,a), (2,a+1), (3,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \)
$0.159931548$
$2.500359038$
0.667056446
\( \frac{520033}{32} a - \frac{141195}{64} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -26 a + 15\) , \( -25 a + 239\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-26a+15\right){x}-25a+239$
36.4-a2
36.4-a
$4$
$6$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
36.4
\( 2^{2} \cdot 3^{2} \)
\( 2^{16} \cdot 3^{3} \)
$1.04973$
$(2,a), (2,a+1), (3,a)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \)
$0.479794644$
$7.501077115$
0.667056446
\( -\frac{7739}{2} a - \frac{8427}{4} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -a\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2-a{x}$
36.4-a3
36.4-a
$4$
$6$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
36.4
\( 2^{2} \cdot 3^{2} \)
\( 2^{17} \cdot 3^{3} \)
$1.04973$
$(2,a), (2,a+1), (3,a)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$0.959589288$
$7.501077115$
0.667056446
\( \frac{21797}{16} a - \frac{5757}{8} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -a\) , \( -a + 1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^3-a{x}-a+1$
36.4-a4
36.4-a
$4$
$6$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
36.4
\( 2^{2} \cdot 3^{2} \)
\( 2^{27} \cdot 3^{9} \)
$1.04973$
$(2,a), (2,a+1), (3,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$0.319863096$
$2.500359038$
0.667056446
\( -\frac{1982707}{4096} a + \frac{3848079}{2048} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 4 a + 30\) , \( 21 a - 27\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^3+\left(4a+30\right){x}+21a-27$
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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.