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
26896.4-a1
26896.4-a
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.4
\( 2^{4} \cdot 41^{2} \)
\( 2^{15} \cdot 41^{4} \)
$3.02768$
$(a), (-a+1), (41)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.863324314$
$1.327233591$
3.738925291
\( -\frac{2602523791}{53792} a - \frac{536659883}{53792} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 18 a + 42\) , \( 138 a - 182\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(18a+42\right){x}+138a-182$
26896.4-a2
26896.4-a
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.4
\( 2^{4} \cdot 41^{2} \)
\( 2^{18} \cdot 41^{2} \)
$3.02768$
$(a), (-a+1), (41)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.931662157$
$2.654467183$
3.738925291
\( -\frac{4462269}{41984} a + \frac{7877935}{41984} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -2 a + 2\) , \( 2 a - 6\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2a+2\right){x}+2a-6$
26896.4-b1
26896.4-b
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.4
\( 2^{4} \cdot 41^{2} \)
\( 2^{15} \cdot 41^{2} \)
$3.02768$
$(a), (-a+1), (41)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \cdot 7 \)
$0.110669009$
$3.131942410$
7.336328972
\( \frac{108311}{5248} a + \frac{4651731}{5248} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( a - 3\) , \( -3 a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a-3\right){x}-3a+1$
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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.