# Properties

 Label 3.13.ar_fe_axs 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: $( 1 - 6 x + 13 x^{2} )( 1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4} )$ Frobenius angles: $\pm0.129998747777$, $\pm0.187167041811$, $\pm0.292104599859$ 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 $A(\F_{q^r})$ 568 4305440 10967735224 23752337500800 51448306585454208 112556148246120910880 247097698041534970160056 542820157999655317229836800 1192549670586296126218272874168 2620004638956813938851726677811200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 149 2271 29113 373192 4831133 62756943 815759857 10604645013 137858965164

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ag $\times$ 2.13.al_cd 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.af_c_bs $2$ (not in LMFDB) 3.13.f_c_abs $2$ (not in LMFDB) 3.13.r_fe_xs $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.af_c_bs $2$ (not in LMFDB) 3.13.f_c_abs $2$ (not in LMFDB) 3.13.r_fe_xs $2$ (not in LMFDB) 3.13.ap_ei_atm $4$ (not in LMFDB) 3.13.ah_y_aco $4$ (not in LMFDB) 3.13.h_y_co $4$ (not in LMFDB) 3.13.p_ei_tm $4$ (not in LMFDB)