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
26896.1-a1
26896.1-a
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.1
\( 2^{4} \cdot 41^{2} \)
\( 2^{11} \cdot 41^{2} \)
$3.02768$
$(a), (41)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$0.065263079$
$3.955430965$
3.122211591
\( -\frac{10082}{41} a + \frac{20438}{41} \)
\( \bigl[0\) , \( -a\) , \( a\) , \( -a - 1\) , \( a + 1\bigr] \)
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-a-1\right){x}+a+1$
26896.1-b1
26896.1-b
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.1
\( 2^{4} \cdot 41^{2} \)
\( 2^{21} \cdot 41^{2} \)
$3.02768$
$(a), (41)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$0.246002109$
$1.714367271$
5.100862964
\( -\frac{115013825}{20992} a + \frac{1953156251}{20992} \)
\( \bigl[0\) , \( a + 1\) , \( a\) , \( 24 a - 32\) , \( 68 a - 65\bigr] \)
${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(24a-32\right){x}+68a-65$
26896.1-c1
26896.1-c
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.1
\( 2^{4} \cdot 41^{2} \)
\( 2^{10} \cdot 41^{2} \)
$3.02768$
$(a), (41)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.752102922$
$3.911486274$
4.447644414
\( \frac{147561}{41} a - \frac{104306}{41} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 3 a - 1\) , \( -a - 2\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(3a-1\right){x}-a-2$
26896.1-c2
26896.1-c
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.1
\( 2^{4} \cdot 41^{2} \)
\( 2^{11} \cdot 41^{4} \)
$3.02768$
$(a), (41)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.504205845$
$1.955743137$
4.447644414
\( -\frac{8155847}{1681} a + \frac{1127168}{1681} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 8 a + 9\) , \( -10 a + 28\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(8a+9\right){x}-10a+28$
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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.