# Properties

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

## 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.

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

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)