Properties

Label 3.13.ar_fb_awy
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 10 x + 48 x^{2} - 130 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.116678169037$, $\pm0.350288405554$
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
$A(\F_{q^r})$ 546 4104828 10506289248 23199716148336 51051603989492106 112406642500855981824 247115407244168646198834 542882604488015191311055872 1192590029730686634236253014496 2620018383061626150738019492675068

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 143 2178 28439 370317 4824716 62761437 815853695 10605003894 137859688343

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ah $\times$ 2.13.ak_bw 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.ad_aj_cy$2$(not in LMFDB)
3.13.d_aj_acy$2$(not in LMFDB)
3.13.r_fb_wy$2$(not in LMFDB)
3.13.ai_bp_agi$3$(not in LMFDB)
3.13.af_l_au$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.ad_aj_cy$2$(not in LMFDB)
3.13.d_aj_acy$2$(not in LMFDB)
3.13.r_fb_wy$2$(not in LMFDB)
3.13.ai_bp_agi$3$(not in LMFDB)
3.13.af_l_au$3$(not in LMFDB)
3.13.ap_eh_atg$6$(not in LMFDB)
3.13.am_dd_ans$6$(not in LMFDB)
3.13.f_l_u$6$(not in LMFDB)
3.13.i_bp_gi$6$(not in LMFDB)
3.13.m_dd_ns$6$(not in LMFDB)
3.13.p_eh_tg$6$(not in LMFDB)