Properties

Label 2.169.abs_bfb
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:  $1 - 44 x + 807 x^{2} - 7436 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0314764500801$, $\pm0.254432080806$
Angle rank:  $2$ (numerical)
Number field:  4.0.8240400.2
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21889 806587761 23293408834276 665420133396508329 19004940840147860278849 542800565135161440920232336 15502932040516451850941308330609 442779261934712221562069253243869769 12646218549766629638622189177629087963236 361188648082378581999893573640011008757678001

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 28240 4825842 815735044 137858325486 23298076313206 3937376192132334 665416606414796164 112455406925602790658 19004963774767520405200

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.8240400.2.
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.bs_bfb$2$(not in LMFDB)