# Properties

 Label 3.13.ar_fb_awy 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: $( 1 - 7 x + 13 x^{2} )( 1 - 10 x + 48 x^{2} - 130 x^{3} + 169 x^{4} )$ Frobenius angles: $\pm0.0772104791556$, $\pm0.116678169037$, $\pm0.350288405554$ 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 $A(\F_{q^r})$ 546 4104828 10506289248 23199716148336 51051603989492106 112406642500855981824 247115407244168646198834 542882604488015191311055872 1192590029730686634236253014496 2620018383061626150738019492675068

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 143 2178 28439 370317 4824716 62761437 815853695 10605003894 137859688343

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ah $\times$ 2.13.ak_bw 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_aj_cy $2$ (not in LMFDB) 3.13.d_aj_acy $2$ (not in LMFDB) 3.13.r_fb_wy $2$ (not in LMFDB) 3.13.ai_bp_agi $3$ (not in LMFDB) 3.13.af_l_au $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ad_aj_cy $2$ (not in LMFDB) 3.13.d_aj_acy $2$ (not in LMFDB) 3.13.r_fb_wy $2$ (not in LMFDB) 3.13.ai_bp_agi $3$ (not in LMFDB) 3.13.af_l_au $3$ (not in LMFDB) 3.13.ap_eh_atg $6$ (not in LMFDB) 3.13.am_dd_ans $6$ (not in LMFDB) 3.13.f_l_u $6$ (not in LMFDB) 3.13.i_bp_gi $6$ (not in LMFDB) 3.13.m_dd_ns $6$ (not in LMFDB) 3.13.p_eh_tg $6$ (not in LMFDB)