# Properties

 Label 3.13.ap_ef_ass 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: $( 1 - 6 x + 13 x^{2} )( 1 - 9 x + 42 x^{2} - 117 x^{3} + 169 x^{4} )$ Frobenius angles: $\pm0.136139978944$, $\pm0.187167041811$, $\pm0.390198274089$ 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 $A(\F_{q^r})$ 688 4650880 10964218432 23480618803200 51274688479675888 112587197950684487680 247202755971073843853488 542872893304061401979289600 1192537349150551687055542497088 2619975166112142019158876065814400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 163 2270 28783 371939 4832464 62783615 815839103 10604535446 137857414363

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ag $\times$ 2.13.aj_bq 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_b_s $2$ (not in LMFDB) 3.13.d_b_as $2$ (not in LMFDB) 3.13.p_ef_ss $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ad_b_s $2$ (not in LMFDB) 3.13.d_b_as $2$ (not in LMFDB) 3.13.p_ef_ss $2$ (not in LMFDB) 3.13.an_dn_apm $4$ (not in LMFDB) 3.13.af_t_aco $4$ (not in LMFDB) 3.13.f_t_co $4$ (not in LMFDB) 3.13.n_dn_pm $4$ (not in LMFDB)