Properties

Label 3.13.aq_er_avd
Base Field $\F_{13}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
L-polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 45 x^{2} - 117 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.215685987913$, $\pm0.344616475996$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 623 4461303 10920532112 23496688030431 51181625711781488 112405265180572883904 247053563007046732215083 542817232264809763704286767 1192545829512406157608235611664 2619996233207791499350984983687168

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 156 2263 28804 371263 4824657 62745730 815755460 10604610859 137858522871

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ah $\times$ 2.13.aj_bt 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
3.13.ac_af_dd$2$(not in LMFDB)
3.13.c_af_add$2$(not in LMFDB)
3.13.q_er_vd$2$(not in LMFDB)
3.13.ah_bo_afo$3$(not in LMFDB)
3.13.ae_n_aj$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.ac_af_dd$2$(not in LMFDB)
3.13.c_af_add$2$(not in LMFDB)
3.13.q_er_vd$2$(not in LMFDB)
3.13.ah_bo_afo$3$(not in LMFDB)
3.13.ae_n_aj$3$(not in LMFDB)
3.13.ao_dz_arr$6$(not in LMFDB)
3.13.al_cy_amm$6$(not in LMFDB)
3.13.e_n_j$6$(not in LMFDB)
3.13.h_bo_fo$6$(not in LMFDB)
3.13.l_cy_mm$6$(not in LMFDB)
3.13.o_dz_rr$6$(not in LMFDB)