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
6966.3-e1
6966.3-e
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
6966.3
\( 2 \cdot 3^{4} \cdot 43 \)
\( 2^{2} \cdot 3^{10} \cdot 43 \)
$2.30903$
$(a), (-a-1), (a-1), (-3a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \cdot 3 \)
$0.207701718$
$2.620434814$
4.618274020
\( -\frac{2847693229}{20898} a - \frac{541607365}{20898} \)
\( \bigl[1\) , \( a\) , \( a\) , \( 12 a - 4\) , \( -18 a - 22\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(12a-4\right){x}-18a-22$
20898.5-a1
20898.5-a
$1$
$1$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
20898.5
\( 2 \cdot 3^{5} \cdot 43 \)
\( 2^{2} \cdot 3^{22} \cdot 43 \)
$3.03885$
$(a), (-a-1), (a-1), (-3a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{3} \)
$0.315615574$
$0.873478271$
3.119001024
\( -\frac{2847693229}{20898} a - \frac{541607365}{20898} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 111 a - 30\) , \( 454 a + 384\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(111a-30\right){x}+454a+384$
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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.