Properties

Label 2.73.abd_no
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:  $1 - 29 x + 352 x^{2} - 2117 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0792175219317$, $\pm0.240494141700$
Angle rank:  $2$ (numerical)
Number field:  4.0.43928.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3536 27679808 151289146112 806595916116224 4297717152587351376 22902059905939874656256 122044986535929230138709968 650377853998363444022600680448 3465863714427874552379183370365696 18469587781046415131072773479708660288

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 45 5193 388902 28403025 2073115645 151334304654 11047396029477 806460059878305 58871586587305782 4297625831777079913

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.43928.1.
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.bd_no$2$(not in LMFDB)