# Properties

 Label 3.13.aq_et_avp 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: $( 1 - 5 x + 13 x^{2} )( 1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4} )$ Frobenius angles: $\pm0.129998747777$, $\pm0.256122854178$, $\pm0.292104599859$ 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 $A(\F_{q^r})$ 639 4601439 11225100852 23833986160959 51390434008460304 112449530624823290304 247013033277756500911683 542782277828473768235592975 1192549044869162504826166878804 2620020318392502099884099810974464

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 160 2323 29212 372773 4826557 62735440 815702932 10604639449 137859790175

## Decomposition and endomorphism algebra

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