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
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
26.1
\( 2 \cdot 13 \)
\( - 2^{4} \cdot 13 \)
$0.83197$
$(-a-1), (-2a+3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$26.23355424$
1.590642869
\( -\frac{4687067}{208} a + \frac{3035213}{52} \)
\( \bigl[1\) , \( -a\) , \( 1\) , \( 13 a - 32\) , \( -28 a + 71\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(13a-32\right){x}-28a+71$
26.1-a2
26.1-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
26.1
\( 2 \cdot 13 \)
\( 2^{2} \cdot 13^{2} \)
$0.83197$
$(-a-1), (-2a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$26.23355424$
1.590642869
\( \frac{345477}{676} a + \frac{466034}{169} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( a + 1\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}$
26.1-a3
26.1-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
26.1
\( 2 \cdot 13 \)
\( 2 \cdot 13 \)
$0.83197$
$(-a-1), (-2a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$26.23355424$
1.590642869
\( -\frac{6134777}{26} a + \frac{8092419}{13} \)
\( \bigl[1\) , \( -a\) , \( 1\) , \( -17 a - 26\) , \( 66 a + 103\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-17a-26\right){x}+66a+103$
26.1-a4
26.1-a
$4$
$4$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
26.1
\( 2 \cdot 13 \)
\( - 2 \cdot 13^{4} \)
$0.83197$
$(-a-1), (-2a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$6.558388562$
1.590642869
\( \frac{147249717681}{57122} a + \frac{115012523207}{28561} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -4 a - 4\) , \( -13 a - 21\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-4\right){x}-13a-21$
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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.