Properties

Label 2.169.abu_bhc
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:  $1 - 46 x + 860 x^{2} - 7774 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0526049868893$, $\pm0.213762271581$
Angle rank:  $2$ (numerical)
Number field:  4.0.417088.1
Galois group:  $D_{4}$
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21602 804501684 23288540053058 665421675820774992 19004994397849796299922 542800789223188122956132244 15502932609596279221187336417426 442779262844000626920624729791321088 12646218550214444006776172026231311273746 361188648080201982004447667018931063900038484

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 124 28166 4824832 815736934 137858713984 23298085931510 3937376336665084 665416607781291070 112455406929584941276 19004963774652992431286

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.417088.1.
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.bu_bhc$2$(not in LMFDB)