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
26.1-a1
26.1-a
$4$
$27$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
26.1
\( 2 \cdot 13 \)
\( 2^{3} \cdot 13^{3} \)
$0.96771$
$(2,a), (13,a+4)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3 \)
$1$
$3.545248488$
0.492823607
\( \frac{16964307415}{17576} a - \frac{7085161553}{17576} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( a - 30\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(4a+4\right){x}+a-30$
26.1-a2
26.1-a
$4$
$27$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
26.1
\( 2 \cdot 13 \)
\( 2^{9} \cdot 13^{9} \)
$0.96771$
$(2,a), (13,a+4)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$1$
$1.181749496$
0.492823607
\( \frac{2187264503235295}{5429503678976} a - \frac{3398685237054473}{5429503678976} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 9 a - 21\) , \( 26 a - 58\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(9a-21\right){x}+26a-58$
26.1-a3
26.1-a
$4$
$27$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
26.1
\( 2 \cdot 13 \)
\( 2 \cdot 13 \)
$0.96771$
$(2,a), (13,a+4)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$10.63574546$
0.492823607
\( \frac{703}{26} a - \frac{2345}{26} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(-a-1\right){x}$
26.1-a4
26.1-a
$4$
$27$
\(\Q(\sqrt{-23}) \)
$2$
$[0, 1]$
26.1
\( 2 \cdot 13 \)
\( 2^{27} \cdot 13^{3} \)
$0.96771$
$(2,a), (13,a+4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3 \)
$1$
$0.393916498$
0.492823607
\( \frac{305308359952290279703}{294876348416} a + \frac{525859732378041384175}{294876348416} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 824 a - 2026\) , \( 19455 a - 22260\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^3+\left(824a-2026\right){x}+19455a-22260$
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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.