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
26.4-a1
26.4-a
$4$
$27$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
26.4
\( 2 \cdot 13 \)
\( 2^{9} \cdot 13^{9} \)
$0.96771$
$(2,a+1), (13,a+8)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$1$
$1.181749496$
0.492823607
\( -\frac{2187264503235295}{5429503678976} a - \frac{605710366909589}{2714751839488} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -10 a - 11\) , \( -26 a - 32\bigr] \)
${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-10a-11\right){x}-26a-32$
26.4-a2
26.4-a
$4$
$27$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
26.4
\( 2 \cdot 13 \)
\( 2 \cdot 13 \)
$0.96771$
$(2,a+1), (13,a+8)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$10.63574546$
0.492823607
\( -\frac{703}{26} a - \frac{821}{13} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2-{x}$
26.4-a3
26.4-a
$4$
$27$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
26.4
\( 2 \cdot 13 \)
\( 2^{3} \cdot 13^{3} \)
$0.96771$
$(2,a+1), (13,a+8)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3 \)
$1$
$3.545248488$
0.492823607
\( -\frac{16964307415}{17576} a + \frac{4939572931}{8788} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a + 9\) , \( -a - 29\bigr] \)
${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-5a+9\right){x}-a-29$
26.4-a4
26.4-a
$4$
$27$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
26.4
\( 2 \cdot 13 \)
\( 2^{27} \cdot 13^{3} \)
$0.96771$
$(2,a+1), (13,a+8)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3 \)
$1$
$0.393916498$
0.492823607
\( -\frac{305308359952290279703}{294876348416} a + \frac{415584046165165831939}{147438174208} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -825 a - 1201\) , \( -19455 a - 2805\bigr] \)
${y}^2+a{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-825a-1201\right){x}-19455a-2805$
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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.