# Properties

 Label 2.13.ao_cx 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: $( 1 - 7 x + 13 x^{2} )^{2}$ Frobenius angles: $\pm0.0772104791556$, $\pm0.0772104791556$ Angle rank: $1$ (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 $A(\F_{q^r})$ 49 21609 4528384 804913641 137542331689 23293210300416 3937628638777729 665450286236357769 112457917496359649536 19005118247840541139449

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 124 2058 28180 370440 4825798 62752536 815772004 10604736114 137859612364

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ah 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-3})$$$)$
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.a_ax $2$ 2.169.abu_bhj 2.13.o_cx $2$ 2.169.abu_bhj 2.13.af_m $3$ (not in LMFDB) 2.13.ac_aj $3$ (not in LMFDB) 2.13.e_be $3$ (not in LMFDB) 2.13.h_bk $3$ (not in LMFDB) 2.13.k_bz $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.13.a_ax $2$ 2.169.abu_bhj 2.13.o_cx $2$ 2.169.abu_bhj 2.13.af_m $3$ (not in LMFDB) 2.13.ac_aj $3$ (not in LMFDB) 2.13.e_be $3$ (not in LMFDB) 2.13.h_bk $3$ (not in LMFDB) 2.13.k_bz $3$ (not in LMFDB) 2.13.a_x $4$ (not in LMFDB) 2.13.am_cj $6$ (not in LMFDB) 2.13.ak_bz $6$ (not in LMFDB) 2.13.aj_bo $6$ (not in LMFDB) 2.13.ah_bk $6$ (not in LMFDB) 2.13.ae_be $6$ (not in LMFDB) 2.13.ad_q $6$ (not in LMFDB) 2.13.a_b $6$ (not in LMFDB) 2.13.a_w $6$ (not in LMFDB) 2.13.c_aj $6$ (not in LMFDB) 2.13.d_q $6$ (not in LMFDB) 2.13.f_m $6$ (not in LMFDB) 2.13.j_bo $6$ (not in LMFDB) 2.13.m_cj $6$ (not in LMFDB) 2.13.a_aw $12$ (not in LMFDB) 2.13.a_ab $12$ (not in LMFDB)