Properties

Label 2.7.af_n
Base Field $\F_{7}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{7}$
Dimension:  $2$
L-polynomial:  $1 - 5 x + 13 x^{2} - 35 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.0616448849068$, $\pm0.511587336964$
Angle rank:  $2$ (numerical)
Number field:  4.0.24389.1
Galois group:  $C_4$
Jacobians:  1

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 23 2369 106421 5375261 280821168 13888046921 677529002537 33205830710069 1628666502870659 79804536835233024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 51 309 2235 16708 118047 822699 5760099 40359873 282518686

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The endomorphism algebra of this simple isogeny class is 4.0.24389.1.
All geometric endomorphisms are defined over $\F_{7}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.7.f_n$2$2.49.b_adf