Properties

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

Learn more about

Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $1 - 47 x + 889 x^{2} - 7943 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.104248499198$, $\pm0.169935694661$
Angle rank:  $2$ (numerical)
Number field:  4.0.306125.1
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
$A(\F_{q^r})$ 21461 803521301 23286978302621 665429532354810245 19005061768865309085696 542801081248467696217329701 15502933538209274579429382082301 442779265181927173505045912793791045 12646218554850518757189492014397674102981 361188648086653413699458027441648772971298816

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 123 28131 4824507 815746563 137859202678 23298098465811 3937376572510707 665416611294768963 112455406970810835843 19004963774992452783406

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.306125.1.
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.bv_bif$2$(not in LMFDB)