Properties

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

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
L-polynomial:  $( 1 - 6 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )$
Frobenius angles:  $\pm0.187167041811$, $\pm0.256122854178$
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
$A(\F_{q^r})$ 72 27360 5025888 832291200 138591237672 23315295467520 3937143790280808 665370955154880000 112452955480771954272 19004889181346053336800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 161 2286 29137 373263 4830374 62744811 815674753 10604268198 137857950761

Decomposition and endomorphism algebra

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