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
26896.5-a1
26896.5-a
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.5
\( 2^{4} \cdot 41^{2} \)
\( 2^{11} \cdot 41^{2} \)
$3.02768$
$(-a+1), (41)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$0.065263079$
$3.955430965$
3.122211591
\( \frac{10082}{41} a + \frac{10356}{41} \)
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( a - 2\) , \( -2 a + 2\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a-2\right){x}-2a+2$
26896.5-b1
26896.5-b
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.5
\( 2^{4} \cdot 41^{2} \)
\( 2^{21} \cdot 41^{2} \)
$3.02768$
$(-a+1), (41)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$0.246002109$
$1.714367271$
5.100862964
\( \frac{115013825}{20992} a + \frac{919071213}{10496} \)
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -22 a - 9\) , \( -46 a + 12\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-22a-9\right){x}-46a+12$
26896.5-c1
26896.5-c
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.5
\( 2^{4} \cdot 41^{2} \)
\( 2^{11} \cdot 41^{4} \)
$3.02768$
$(-a+1), (41)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.504205845$
$1.955743137$
4.447644414
\( \frac{8155847}{1681} a - \frac{7028679}{1681} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -8 a + 17\) , \( 10 a + 18\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8a+17\right){x}+10a+18$
26896.5-c2
26896.5-c
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.5
\( 2^{4} \cdot 41^{2} \)
\( 2^{10} \cdot 41^{2} \)
$3.02768$
$(-a+1), (41)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.752102922$
$3.911486274$
4.447644414
\( -\frac{147561}{41} a + 1055 \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -3 a + 2\) , \( a - 3\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+2\right){x}+a-3$
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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.