Properties

Label 2.181.abu_bic
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:  $1 - 46 x + 886 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.112775809299$, $\pm0.219413980321$
Angle rank:  $2$ (numerical)
Number field:  4.0.638000.2
Galois group:  $D_{4}$
Jacobians:  48

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 48 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25276 1062097520 35161561916956 1151991091987915520 37738794327587194977916 1236354618347055078294798320 40504199693028004271465112291676 1326958064217100461291533141826744320 43472473122842955767935397528873245771516 1424201691978533439793078199515795901980950000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32418 5929696 1073333838 194265261456 35161841040978 6364291035142456 1151936658326587038 208500535066112619256 37738596846994879205698

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.638000.2.
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_bic$2$(not in LMFDB)