Properties

Label 2.73.abc_nc
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:  $1 - 28 x + 340 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.142062947302$, $\pm0.236464216789$
Angle rank:  $2$ (numerical)
Number field:  4.0.465152.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3598 27855716 151519958254 806822874858896 4297900337682289198 22902183069747610775972 122045053051779885637064014 650377878295208539017802846208 3465863713574889772379357346357358 18469587769181502379710952143644426916

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5226 389494 28411014 2073204006 151335118506 11047402050430 806460090006078 58871586572816878 4297625829016273546

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.465152.1.
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.bc_nc$2$(not in LMFDB)