Properties

Label 2.181.abx_bky
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:  $( 1 - 26 x + 181 x^{2} )( 1 - 23 x + 181 x^{2} )$
Frobenius angles:  $\pm0.0828936782352$, $\pm0.173686936480$
Angle rank:  $2$ (numerical)
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24804 1057642560 35143243402176 1151941551823146240 37738708209327963498804 1236354581202761315602944000 40504200050248004980084185238644 1326958065691480231979711021662786560 43472473125847748392377503408285560545216 1424201691979719109153346875283106135780264000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 133 32281 5926606 1073287681 194264818153 35161839984598 6364291091271253 1151936659606500961 208500535080524057686 37738596847026297156001

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.aba $\times$ 1.181.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ad_ajc$2$(not in LMFDB)
2.181.d_ajc$2$(not in LMFDB)
2.181.bx_bky$2$(not in LMFDB)
2.181.aq_ht$3$(not in LMFDB)
2.181.ae_acx$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.ad_ajc$2$(not in LMFDB)
2.181.d_ajc$2$(not in LMFDB)
2.181.bx_bky$2$(not in LMFDB)
2.181.aq_ht$3$(not in LMFDB)
2.181.ae_acx$3$(not in LMFDB)
2.181.abq_bet$6$(not in LMFDB)
2.181.abe_ud$6$(not in LMFDB)
2.181.e_acx$6$(not in LMFDB)
2.181.q_ht$6$(not in LMFDB)
2.181.be_ud$6$(not in LMFDB)
2.181.bq_bet$6$(not in LMFDB)