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
26896.2-a1
26896.2-a
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.2
\( 2^{4} \cdot 41^{2} \)
\( 2^{15} \cdot 41^{4} \)
$3.02768$
$(a), (-a+1), (41)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1.863324314$
$1.327233591$
3.738925291
\( \frac{2602523791}{53792} a - \frac{1569591837}{26896} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -20 a + 63\) , \( -77 a - 67\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a+63\right){x}-77a-67$
26896.2-a2
26896.2-a
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.2
\( 2^{4} \cdot 41^{2} \)
\( 2^{18} \cdot 41^{2} \)
$3.02768$
$(a), (-a+1), (41)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.931662157$
$2.654467183$
3.738925291
\( \frac{4462269}{41984} a + \frac{1707833}{20992} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 3\) , \( -a - 7\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+3{x}-a-7$
26896.2-b1
26896.2-b
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
26896.2
\( 2^{4} \cdot 41^{2} \)
\( 2^{15} \cdot 41^{2} \)
$3.02768$
$(a), (-a+1), (41)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \cdot 7 \)
$0.110669009$
$3.131942410$
7.336328972
\( -\frac{108311}{5248} a + \frac{2380021}{2624} \)
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -2 a\) , \( 4\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}-2a{x}+4$
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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.