Properties

Label 2.181.abu_bia
Base Field $\F_{181}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 46 x + 884 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0978554663067$, $\pm0.226927340693$
Angle rank:  $2$ (numerical)
Number field:  4.0.16097088.1
Galois group:  $D_{4}$
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25274 1061962932 35159923103354 1151980521528452688 37738747233877331169434 1236354459725412691355255508 40504199284856291567904093990746 1326958063488344414927514033801704448 43472473122465875888320546487844151609706 1424201691981962717923354555970970289420990932

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32414 5929420 1073323990 194265019036 35161836529790 6364290971007784 1151936657693951518 208500535064304087304 37738596847085748459374

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.16097088.1.
All geometric endomorphisms are defined over $\F_{181}$.

Base change

This is a primitive isogeny class.

Twists

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