Properties

Label 2.73.abe_of
Base Field $\F_{73}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $1 - 30 x + 369 x^{2} - 2190 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0896851289724$, $\pm0.207445605396$
Angle rank:  $2$ (numerical)
Number field:  4.0.155200.2
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3479 27550201 151194570716 806590568251321 4297782867694392839 22902146748843298512016 122045053743127283027228711 650377886722839255284870502825 3465863718922499496911830353943964 18469587771693039120756317641676530921

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 44 5168 388658 28402836 2073147344 151334878502 11047402113008 806460100456228 58871586663652034 4297625829600674528

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.155200.2.
All geometric endomorphisms are defined over $\F_{73}$.

Base change

This is a primitive isogeny class.

Twists

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