Properties

Label 2.181.abz_bmy
Base Field $\F_{181}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $( 1 - 26 x + 181 x^{2} )( 1 - 25 x + 181 x^{2} )$
Frobenius angles:  $\pm0.0828936782352$, $\pm0.120568372405$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24492 1054527552 35129186256528 1151897248061164800 37738605754100099474652 1236354437080897182145843200 40504200155264902926413670063132 1326958067307580644211705816891315200 43472473132842425453314184639531592925968 1424201692001357142722879622414976053878632512

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 131 32185 5924234 1073246401 194264290751 35161835885782 6364291107772211 1151936661009443041 208500535114071583394 37738596847599663295105

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.aba $\times$ 1.181.az 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.ab_alc$2$(not in LMFDB)
2.181.b_alc$2$(not in LMFDB)
2.181.bz_bmy$2$(not in LMFDB)
2.181.as_hf$3$(not in LMFDB)
2.181.ag_aej$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.ab_alc$2$(not in LMFDB)
2.181.b_alc$2$(not in LMFDB)
2.181.bz_bmy$2$(not in LMFDB)
2.181.as_hf$3$(not in LMFDB)
2.181.ag_aej$3$(not in LMFDB)
2.181.abs_bgf$6$(not in LMFDB)
2.181.abg_ur$6$(not in LMFDB)
2.181.g_aej$6$(not in LMFDB)
2.181.s_hf$6$(not in LMFDB)
2.181.bg_ur$6$(not in LMFDB)
2.181.bs_bgf$6$(not in LMFDB)