Properties

Label 2.169.abw_bjc
Base Field $\F_{13^{2}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 912 x^{2} - 8112 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0676966056373$, $\pm0.164966217013$
Angle rank:  $2$ (numerical)
Number field:  4.0.319744.3
Galois group:  $D_{4}$
Jacobians:  12

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21314 802131076 23280718508642 665408312165921296 19005001287878055651074 542800929833940016331228164 15502933199020570246714861216034 442779264500695321507682933532524544 12646218553647734868744610322313327293762 361188648084922927460690755824233161828447876

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 122 28082 4823210 815720550 137858763962 23298091966802 3937376486364842 665416610271001534 112455406960115183930 19004963774901398348402

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.319744.3.
All geometric endomorphisms are defined over $\F_{13^{2}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.169.bw_bjc$2$(not in LMFDB)