Properties

Label 2.181.abu_bhv
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:  $1 - 46 x + 879 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0578498171782$, $\pm0.241355956375$
Angle rank:  $2$ (numerical)
Number field:  4.0.1165968.2
Galois group:  $D_{4}$
Jacobians:  30

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 30 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25269 1061626497 35155826162064 1151954020355506233 37738627935847993326309 1236354046254633884760695808 40504198137903136147249864920381 1326958060934658882239345817807222633 43472473118059525496498886362991655132176 1424201691976701411028471034612338353652386657

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32404 5928730 1073299300 194264404936 35161824770710 6364290790790824 1151936655477088708 208500535043170566514 37738596846946333978324

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.1165968.2.
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_bhv$2$(not in LMFDB)