Properties

Label 2.181.abu_bib
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:  $1 - 46 x + 885 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.105257672036$, $\pm0.223354207626$
Angle rank:  $2$ (numerical)
Number field:  4.0.530496.5
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25275 1062030225 35160742507500 1151985808901714025 37738770825410933806875 1236354539519145417724170000 40504199492544819903352152995475 1326958063873445730099903689877753225 43472473122751460817131066346206023207500 1424201691980628059900160794148363105905930625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32416 5929558 1073328916 194265140476 35161838799118 6364291003641196 1151936658028259236 208500535065673795678 37738596847050382596976

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.530496.5.
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_bib$2$(not in LMFDB)