Properties

Label 2.181.abz_bmx
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:  $1 - 51 x + 1011 x^{2} - 9231 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0467121644153$, $\pm0.139008714891$
Angle rank:  $2$ (numerical)
Number field:  4.0.50125.1
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24491 1054460005 35128277447231 1151890423380452005 37738568154960421158416 1236354267375807197377086805 40504199492711841015405998056151 1326958065002999300604090776449398405 43472473125583976609943105146194167462131 1424201691980506209640360423146178676020000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 131 32183 5924081 1073240043 194264097206 35161831059383 6364291003667441 1151936659008828403 208500535079258968451 37738596847047153800198

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.50125.1.
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.bz_bmx$2$(not in LMFDB)