# Properties

 Label 2.169.abv_big Base Field $\F_{13^{2}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{13^{2}}$ Dimension: $2$ L-polynomial: $( 1 - 24 x + 169 x^{2} )( 1 - 23 x + 169 x^{2} )$ Frobenius angles: $\pm0.125665916378$, $\pm0.154420958311$ 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 $A(\F_{q^r})$ 21462 803580204 23287660050816 665433838241625600 19005081174646389472902 542801150339783781263440896 15502933740135738131364469068582 442779265664390413475874828160358400 12646218555725689223184224058234865186176 361188648087432922279035773302689767766343404

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 123 28133 4824648 815751841 137859343443 23298101431346 3937376623795227 665416612019823361 112455406978593213672 19004963775033468835253

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
 The isogeny class factors as 1.169.ay $\times$ 1.169.ax 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 $\F_{13^{2}}$.

## 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 2.169.ab_aig $2$ (not in LMFDB) 2.169.b_aig $2$ (not in LMFDB) 2.169.bv_big $2$ (not in LMFDB) 2.169.ax_mc $3$ (not in LMFDB) 2.169.ac_ahi $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.169.ab_aig $2$ (not in LMFDB) 2.169.b_aig $2$ (not in LMFDB) 2.169.bv_big $2$ (not in LMFDB) 2.169.ax_mc $3$ (not in LMFDB) 2.169.ac_ahi $3$ (not in LMFDB) 2.169.abh_vw $4$ (not in LMFDB) 2.169.an_ee $4$ (not in LMFDB) 2.169.n_ee $4$ (not in LMFDB) 2.169.bh_vw $4$ (not in LMFDB) 2.169.abu_bhi $6$ (not in LMFDB) 2.169.az_ny $6$ (not in LMFDB) 2.169.c_ahi $6$ (not in LMFDB) 2.169.x_mc $6$ (not in LMFDB) 2.169.z_ny $6$ (not in LMFDB) 2.169.bu_bhi $6$ (not in LMFDB) 2.169.abg_vm $12$ (not in LMFDB) 2.169.am_eo $12$ (not in LMFDB) 2.169.al_nk $12$ (not in LMFDB) 2.169.aj_mq $12$ (not in LMFDB) 2.169.j_mq $12$ (not in LMFDB) 2.169.l_nk $12$ (not in LMFDB) 2.169.m_eo $12$ (not in LMFDB) 2.169.bg_vm $12$ (not in LMFDB)