# Properties

 Label 2.13.aj_bu Base Field $\F_{13}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{13}$ Dimension: $2$ L-polynomial: $( 1 - 5 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$ Frobenius angles: $\pm0.256122854178$, $\pm0.312832958189$ Angle rank: $2$ (numerical) Jacobians: 0

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary. $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## 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 $A(\F_{q^r})$ 90 30780 5193720 832291200 138056202450 23276009352960 3935763223779330 665370955154880000 112455979023092576760 19005077510025702543900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 181 2360 29137 371825 4822234 62722805 815674753 10604553320 137859316861

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.af $\times$ 1.13.ae 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 2.13.ab_g $2$ 2.169.l_nk 2.13.b_g $2$ 2.169.l_nk 2.13.j_bu $2$ 2.169.l_nk 2.13.ag_bi $3$ (not in LMFDB) 2.13.d_ac $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.13.ab_g $2$ 2.169.l_nk 2.13.b_g $2$ 2.169.l_nk 2.13.j_bu $2$ 2.169.l_nk 2.13.ag_bi $3$ (not in LMFDB) 2.13.d_ac $3$ (not in LMFDB) 2.13.al_ce $4$ (not in LMFDB) 2.13.ab_ae $4$ (not in LMFDB) 2.13.b_ae $4$ (not in LMFDB) 2.13.l_ce $4$ (not in LMFDB) 2.13.al_cc $6$ (not in LMFDB) 2.13.ad_ac $6$ (not in LMFDB) 2.13.ac_s $6$ (not in LMFDB) 2.13.c_s $6$ (not in LMFDB) 2.13.g_bi $6$ (not in LMFDB) 2.13.l_cc $6$ (not in LMFDB) 2.13.an_cq $12$ (not in LMFDB) 2.13.ai_bm $12$ (not in LMFDB) 2.13.ae_o $12$ (not in LMFDB) 2.13.ab_aq $12$ (not in LMFDB) 2.13.b_aq $12$ (not in LMFDB) 2.13.e_o $12$ (not in LMFDB) 2.13.i_bm $12$ (not in LMFDB) 2.13.n_cq $12$ (not in LMFDB)