Properties

Label 2.7.ag_v
Base Field $\F_{7}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{7}$
Dimension:  $2$
L-polynomial:  $1 - 6 x + 21 x^{2} - 42 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.185925252552$, $\pm0.403118263531$
Angle rank:  $2$ (numerical)
Number field:  4.0.13888.1
Galois group:  $D_{4}$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

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

Point counts

This isogeny class contains the Jacobians of 2 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 2737 130916 5848969 282342503 13896471568 680365917527 33255091162377 1627947385063652 79774236353790097

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 56 380 2436 16802 118118 826142 5768644 40342052 282411416

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The endomorphism algebra of this simple isogeny class is 4.0.13888.1.
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.g_v$2$2.49.g_bj