Properties

Label 2.169.abv_bid
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:  $1 - 47 x + 887 x^{2} - 7943 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0738822392977$, $\pm0.185751622566$
Angle rank:  $2$ (numerical)
Number field:  4.0.1240629.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21459 803403501 23285614822227 665420910811195941 19005022762936426138224 542800941032059740838587429 15502933119425606590811877797979 442779264130864598597084153772781989 12646218552686199868611550903280740664307 361188648083380578164030039351771178021739776

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 123 28127 4824225 815735995 137858919738 23298092447447 3937376466149613 665416609715213299 112455406951564816935 19004963774820243271502

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.1240629.1.
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.bv_bid$2$(not in LMFDB)