Properties

Label 2.181.abw_bkc
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:  $( 1 - 24 x + 181 x^{2} )^{2}$
Frobenius angles:  $\pm0.149335043618$, $\pm0.149335043618$
Angle rank:  $1$ (numerical)
Jacobians:  13

This isogeny class is not 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 13 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24964 1059372304 35152448102500 1151979003524911104 37738836482772472975684 1236354961193954418216490000 40504201016372596683469625079844 1326958067686521650832563947218468864 43472473128498645335793145903627245002500 1424201691977667603367860389237713356249063184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 134 32334 5928158 1073322574 194265478454 35161850791518 6364291243075214 1151936661338402974 208500535093238159078 37738596846971936211054

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-37}) \)$)$
All geometric endomorphisms are defined over $\F_{181}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.a_aig$2$(not in LMFDB)
2.181.bw_bkc$2$(not in LMFDB)
2.181.y_pf$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.a_aig$2$(not in LMFDB)
2.181.bw_bkc$2$(not in LMFDB)
2.181.y_pf$3$(not in LMFDB)
2.181.a_ig$4$(not in LMFDB)
2.181.ay_pf$6$(not in LMFDB)