Properties

 Label 2.13.an_cq 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: $( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )$ Frobenius angles: $\pm0.0772104791556$, $\pm0.187167041811$ 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 $A(\F_{q^r})$ 56 23520 4715648 817084800 138143507096 23315295467520 3938060927158232 665433838241625600 112455465963248062592 19004946846716043141600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 137 2146 28609 372061 4830374 62759425 815751841 10604504938 137858369057

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ah $\times$ 1.13.ag 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 2.13.ab_aq $2$ 2.169.abh_vw 2.13.b_aq $2$ 2.169.abh_vw 2.13.n_cq $2$ 2.169.abh_vw 2.13.ae_o $3$ (not in LMFDB) 2.13.ab_ae $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.13.ab_aq $2$ 2.169.abh_vw 2.13.b_aq $2$ 2.169.abh_vw 2.13.n_cq $2$ 2.169.abh_vw 2.13.ae_o $3$ (not in LMFDB) 2.13.ab_ae $3$ (not in LMFDB) 2.13.al_cc $4$ (not in LMFDB) 2.13.ad_ac $4$ (not in LMFDB) 2.13.d_ac $4$ (not in LMFDB) 2.13.l_cc $4$ (not in LMFDB) 2.13.al_ce $6$ (not in LMFDB) 2.13.ai_bm $6$ (not in LMFDB) 2.13.b_ae $6$ (not in LMFDB) 2.13.e_o $6$ (not in LMFDB) 2.13.i_bm $6$ (not in LMFDB) 2.13.l_ce $6$ (not in LMFDB) 2.13.aj_bu $12$ (not in LMFDB) 2.13.ag_bi $12$ (not in LMFDB) 2.13.ac_s $12$ (not in LMFDB) 2.13.ab_g $12$ (not in LMFDB) 2.13.b_g $12$ (not in LMFDB) 2.13.c_s $12$ (not in LMFDB) 2.13.g_bi $12$ (not in LMFDB) 2.13.j_bu $12$ (not in LMFDB)