Properties

Label 2.181.abx_bkw
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:  $1 - 49 x + 958 x^{2} - 8869 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0510791052243$, $\pm0.186092366958$
Angle rank:  $2$ (numerical)
Number field:  4.0.1177964.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24802 1057507676 35141497343992 1151929169285599616 37738645003174932161962 1236354322465217596955535104 40504199156669776913824058997658 1326958063024981273589998570281342464 43472473118927175227615783496853625036152 1424201691964266916773951026551181138514849276

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 133 32277 5926312 1073276145 194264492793 35161832626122 6364290950866261 1151936657291704449 208500535047331945432 37738596846616843872877

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.1177964.1.
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.bx_bkw$2$(not in LMFDB)