# Properties

 Label 3.13.aq_er_avd 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: $( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 45 x^{2} - 117 x^{3} + 169 x^{4} )$ Frobenius angles: $\pm0.0772104791556$, $\pm0.215685987913$, $\pm0.344616475996$ 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 $A(\F_{q^r})$ 623 4461303 10920532112 23496688030431 51181625711781488 112405265180572883904 247053563007046732215083 542817232264809763704286767 1192545829512406157608235611664 2619996233207791499350984983687168

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 156 2263 28804 371263 4824657 62745730 815755460 10604610859 137858522871

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ah $\times$ 2.13.aj_bt 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_af_dd $2$ (not in LMFDB) 3.13.c_af_add $2$ (not in LMFDB) 3.13.q_er_vd $2$ (not in LMFDB) 3.13.ah_bo_afo $3$ (not in LMFDB) 3.13.ae_n_aj $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ac_af_dd $2$ (not in LMFDB) 3.13.c_af_add $2$ (not in LMFDB) 3.13.q_er_vd $2$ (not in LMFDB) 3.13.ah_bo_afo $3$ (not in LMFDB) 3.13.ae_n_aj $3$ (not in LMFDB) 3.13.ao_dz_arr $6$ (not in LMFDB) 3.13.al_cy_amm $6$ (not in LMFDB) 3.13.e_n_j $6$ (not in LMFDB) 3.13.h_bo_fo $6$ (not in LMFDB) 3.13.l_cy_mm $6$ (not in LMFDB) 3.13.o_dz_rr $6$ (not in LMFDB)