Properties

Label 2.13.al_cc
Base Field $\F_{13}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.312832958189$
Angle rank:  $2$ (numerical)
Jacobians:  1

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 contains the Jacobians of 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 70 26460 4873120 817084800 137610200350 23276009352960 3936680039061070 665433838241625600 112458489573068467360 19005135175967126514300

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 157 2220 28609 370623 4822234 62737419 815751841 10604790060 137859735157

Decomposition and endomorphism algebra

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