Properties

Label 2.169.abw_bjb
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:  $1 - 48 x + 911 x^{2} - 8112 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0457381254353$, $\pm0.172659114562$
Angle rank:  $2$ (numerical)
Number field:  4.0.359568.2
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21313 802072129 23280022209316 665403768037744713 19004979781804288431313 542800847477319326149144336 15502932929867310794785327216897 442779263728511907464348139507446793 12646218551674589565262864250808785020132 361188648080408976878303618099631417992316769

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 122 28080 4823066 815714980 137858607962 23298088431894 3937376418006314 665416609110550468 112455406942569159626 19004963774663884052880

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.359568.2.
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.bw_bjb$2$(not in LMFDB)