Properties

Label 2.169.abs_bfg
Base Field $\F_{13^{2}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $1 - 44 x + 812 x^{2} - 7436 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0810217339920$, $\pm0.242057894147$
Angle rank:  $2$ (numerical)
Number field:  4.0.22022400.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21894 806881476 23296599022086 665438513111666064 19005014539488235056774 542800794122247861189997956 15502932622763690885605931683974 442779263200089689306368657313009664 12646218552283399465465990410707792793126 361188648087573451340182857993522294475110276

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 28250 4826502 815757574 137858860086 23298086141786 3937376340009294 665416608316428094 112455406947982949118 19004963775040863169850

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.22022400.1.
All geometric endomorphisms are defined over $\F_{13^{2}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.169.bs_bfg$2$(not in LMFDB)