# Properties

 Label 3.13.as_fp_azv 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: $( 1 - 7 x + 13 x^{2} )( 1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4} )$ Frobenius angles: $\pm0.0772104791556$, $\pm0.129998747777$, $\pm0.292104599859$ 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 $A(\F_{q^r})$ 497 3955623 10532193392 23398526640111 51224412916463472 112449530624823290304 247070573660859256322357 542833575266085419511276207 1192575668211041284187628658544 2620028268159512012487928792781568

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -4 136 2183 28684 371571 4826557 62750054 815780020 10604876189 137860208471

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ah $\times$ 2.13.al_cd 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.ae_aj_dv $2$ (not in LMFDB) 3.13.e_aj_adv $2$ (not in LMFDB) 3.13.s_fp_zv $2$ (not in LMFDB) 3.13.aj_bu_agu $3$ (not in LMFDB) 3.13.ag_n_al $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ae_aj_dv $2$ (not in LMFDB) 3.13.e_aj_adv $2$ (not in LMFDB) 3.13.s_fp_zv $2$ (not in LMFDB) 3.13.aj_bu_agu $3$ (not in LMFDB) 3.13.ag_n_al $3$ (not in LMFDB) 3.13.aq_et_avp $6$ (not in LMFDB) 3.13.an_dm_apg $6$ (not in LMFDB) 3.13.g_n_l $6$ (not in LMFDB) 3.13.j_bu_gu $6$ (not in LMFDB) 3.13.n_dm_pg $6$ (not in LMFDB) 3.13.q_et_vp $6$ (not in LMFDB)