Properties

Label 2.169.abv_bic
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:  $1 - 47 x + 886 x^{2} - 7943 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0585395387306$, $\pm0.191425177757$
Angle rank:  $2$ (numerical)
Number field:  4.0.1413788.1
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
$A(\F_{q^r})$ 21458 803344604 23284933090016 665416595154354368 19005003162788553065538 542800869906408642101970176 15502932902552857335103158299282 442779263562039767245167652705465088 12646218551394779377627094698080897673952 361188648080869407150446917304838844580311644

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 123 28125 4824084 815730705 137858777563 23298089394594 3937376411069091 665416608860373153 112455406940080971684 19004963774688110895805

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.1413788.1.
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_bic$2$(not in LMFDB)