# Properties

 Label 3.13.ap_ee_asm Base Field $\F_{13}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{13}$ Dimension: $3$ L-polynomial: $( 1 - 6 x + 13 x^{2} )( 1 - 9 x + 41 x^{2} - 117 x^{3} + 169 x^{4} )$ Frobenius angles: $\pm0.109149799241$, $\pm0.187167041811$, $\pm0.400911184348$ Angle rank: $3$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 680 4583200 10829381480 23350945680000 51206443416310400 112568218669671623200 247196800994063115498920 542866357155795385896000000 1192536010021171371049232913320 2619982089030695746857167994880000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 161 2243 28625 371444 4831649 62782103 815829281 10604523539 137857778636

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ag $\times$ 2.13.aj_bp 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 $\F_{13}$.

## 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 3.13.ad_a_m $2$ (not in LMFDB) 3.13.d_a_am $2$ (not in LMFDB) 3.13.p_ee_sm $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ad_a_m $2$ (not in LMFDB) 3.13.d_a_am $2$ (not in LMFDB) 3.13.p_ee_sm $2$ (not in LMFDB) 3.13.an_dm_api $4$ (not in LMFDB) 3.13.af_s_acs $4$ (not in LMFDB) 3.13.f_s_cs $4$ (not in LMFDB) 3.13.n_dm_pi $4$ (not in LMFDB)