Properties

Label 2.13.an_cq
Base Field $\F_{13}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 56 23520 4715648 817084800 138143507096 23315295467520 3938060927158232 665433838241625600 112455465963248062592 19004946846716043141600

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)