Properties

Label 2.169.abv_big
Base Field $\F_{13^{2}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 24 x + 169 x^{2} )( 1 - 23 x + 169 x^{2} )$
Frobenius angles:  $\pm0.125665916378$, $\pm0.154420958311$
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
$A(\F_{q^r})$ 21462 803580204 23287660050816 665433838241625600 19005081174646389472902 542801150339783781263440896 15502933740135738131364469068582 442779265664390413475874828160358400 12646218555725689223184224058234865186176 361188648087432922279035773302689767766343404

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 123 28133 4824648 815751841 137859343443 23298101431346 3937376623795227 665416612019823361 112455406978593213672 19004963775033468835253

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The isogeny class factors as 1.169.ay $\times$ 1.169.ax 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 $\F_{13^{2}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.169.ab_aig$2$(not in LMFDB)
2.169.b_aig$2$(not in LMFDB)
2.169.bv_big$2$(not in LMFDB)
2.169.ax_mc$3$(not in LMFDB)
2.169.ac_ahi$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.169.ab_aig$2$(not in LMFDB)
2.169.b_aig$2$(not in LMFDB)
2.169.bv_big$2$(not in LMFDB)
2.169.ax_mc$3$(not in LMFDB)
2.169.ac_ahi$3$(not in LMFDB)
2.169.abh_vw$4$(not in LMFDB)
2.169.an_ee$4$(not in LMFDB)
2.169.n_ee$4$(not in LMFDB)
2.169.bh_vw$4$(not in LMFDB)
2.169.abu_bhi$6$(not in LMFDB)
2.169.az_ny$6$(not in LMFDB)
2.169.c_ahi$6$(not in LMFDB)
2.169.x_mc$6$(not in LMFDB)
2.169.z_ny$6$(not in LMFDB)
2.169.bu_bhi$6$(not in LMFDB)
2.169.abg_vm$12$(not in LMFDB)
2.169.am_eo$12$(not in LMFDB)
2.169.al_nk$12$(not in LMFDB)
2.169.aj_mq$12$(not in LMFDB)
2.169.j_mq$12$(not in LMFDB)
2.169.l_nk$12$(not in LMFDB)
2.169.m_eo$12$(not in LMFDB)
2.169.bg_vm$12$(not in LMFDB)