Properties

Label 2.13.ao_cx
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:  $( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 49 21609 4528384 804913641 137542331689 23293210300416 3937628638777729 665450286236357769 112457917496359649536 19005118247840541139449

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 124 2058 28180 370440 4825798 62752536 815772004 10604736114 137859612364

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ah 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
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.a_ax$2$2.169.abu_bhj
2.13.o_cx$2$2.169.abu_bhj
2.13.af_m$3$(not in LMFDB)
2.13.ac_aj$3$(not in LMFDB)
2.13.e_be$3$(not in LMFDB)
2.13.h_bk$3$(not in LMFDB)
2.13.k_bz$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.13.a_ax$2$2.169.abu_bhj
2.13.o_cx$2$2.169.abu_bhj
2.13.af_m$3$(not in LMFDB)
2.13.ac_aj$3$(not in LMFDB)
2.13.e_be$3$(not in LMFDB)
2.13.h_bk$3$(not in LMFDB)
2.13.k_bz$3$(not in LMFDB)
2.13.a_x$4$(not in LMFDB)
2.13.am_cj$6$(not in LMFDB)
2.13.ak_bz$6$(not in LMFDB)
2.13.aj_bo$6$(not in LMFDB)
2.13.ah_bk$6$(not in LMFDB)
2.13.ae_be$6$(not in LMFDB)
2.13.ad_q$6$(not in LMFDB)
2.13.a_b$6$(not in LMFDB)
2.13.a_w$6$(not in LMFDB)
2.13.c_aj$6$(not in LMFDB)
2.13.d_q$6$(not in LMFDB)
2.13.f_m$6$(not in LMFDB)
2.13.j_bo$6$(not in LMFDB)
2.13.m_cj$6$(not in LMFDB)
2.13.a_aw$12$(not in LMFDB)
2.13.a_ab$12$(not in LMFDB)