# Properties

 Label 3.13.aq_en_aub 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: $( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 41 x^{2} - 117 x^{3} + 169 x^{4} )$ Frobenius angles: $\pm0.0772104791556$, $\pm0.109149799241$, $\pm0.400911184348$ 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 $A(\F_{q^r})$ 595 4210815 10399333840 23003113884975 50983602291823600 112461589614792922560 247169665734669259945615 542879775564162421878399375 1192562007348115729035492404560 2620005718030021365669969970483200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 148 2155 28196 369823 4827073 62775214 815849444 10604754715 137859021943

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ah $\times$ 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.ac_aj_cb $2$ (not in LMFDB) 3.13.c_aj_acb $2$ (not in LMFDB) 3.13.q_en_ub $2$ (not in LMFDB) 3.13.ah_bk_afw $3$ (not in LMFDB) 3.13.ae_j_abd $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ac_aj_cb $2$ (not in LMFDB) 3.13.c_aj_acb $2$ (not in LMFDB) 3.13.q_en_ub $2$ (not in LMFDB) 3.13.ah_bk_afw $3$ (not in LMFDB) 3.13.ae_j_abd $3$ (not in LMFDB) 3.13.ao_dv_aqx $6$ (not in LMFDB) 3.13.al_cu_ame $6$ (not in LMFDB) 3.13.e_j_bd $6$ (not in LMFDB) 3.13.h_bk_fw $6$ (not in LMFDB) 3.13.l_cu_me $6$ (not in LMFDB) 3.13.o_dv_qx $6$ (not in LMFDB)