Properties

 Label 3.13.ap_dz_are 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: $( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 34 x^{2} - 104 x^{3} + 169 x^{4} )$ Frobenius angles: $\pm0.0772104791556$, $\pm0.104164352389$, $\pm0.448054596667$ 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 $A(\F_{q^r})$ 644 4273584 10238497472 22856905042944 51016152313775124 112539965532274732032 247170331084403268714116 542837458761077365592211456 1192546278982659896218419027392 2620019421645100182730662587955504

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 151 2120 28015 370059 4830436 62775383 815785855 10604614856 137859742991

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ah $\times$ 2.13.ai_bi 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.ab_aj_be $2$ (not in LMFDB) 3.13.b_aj_abe $2$ (not in LMFDB) 3.13.p_dz_re $2$ (not in LMFDB) 3.13.ag_bf_afk $3$ (not in LMFDB) 3.13.ad_h_abm $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ab_aj_be $2$ (not in LMFDB) 3.13.b_aj_abe $2$ (not in LMFDB) 3.13.p_dz_re $2$ (not in LMFDB) 3.13.ag_bf_afk $3$ (not in LMFDB) 3.13.ad_h_abm $3$ (not in LMFDB) 3.13.an_dj_aoo $6$ (not in LMFDB) 3.13.ak_cl_akq $6$ (not in LMFDB) 3.13.d_h_bm $6$ (not in LMFDB) 3.13.g_bf_fk $6$ (not in LMFDB) 3.13.k_cl_kq $6$ (not in LMFDB) 3.13.n_dj_oo $6$ (not in LMFDB)