Properties

Label 2.169.abs_bfe
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:  $1 - 44 x + 810 x^{2} - 7436 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0647393693303$, $\pm0.247372633299$
Angle rank:  $2$ (numerical)
Number field:  4.0.330048.1
Galois group:  $D_{4}$
Jacobians:  56

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 56 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21892 806763984 23295322932388 665431170999309312 19004985241716052615972 542800704283991919221670864 15502932401594143951032876344836 442779262754672119686378121461055488 12646218551535717014302389853296563681476 361188648086440020414505010982983670669522384

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 28246 4826238 815748574 137858647566 23298082285750 3937376283837486 665416607647046590 112455406941334247454 19004963774981224491286

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.330048.1.
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_bfe$2$(not in LMFDB)