Properties

Label 2.73.abe_oe
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:  $1 - 30 x + 368 x^{2} - 2190 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0650840807172$, $\pm0.217019455223$
Angle rank:  $2$ (numerical)
Number field:  4.0.201024.4
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
$A(\F_{q^r})$ 3478 27538804 151159364806 806530164455376 4297709478118732918 22902076910953681874836 122044999414449575223647782 650377851840945930529664676864 3465863700893048512786809001235494 18469587764934916610553924726341530324

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 44 5166 388568 28400710 2073111944 151334417022 11047397195228 806460057203134 58871586357401564 4297625828028149886

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.201024.4.
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_oe$2$(not in LMFDB)