Properties

Label 2.73.aba_ls
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:  $1 - 26 x + 304 x^{2} - 1898 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0960067538857$, $\pm0.308228869049$
Angle rank:  $2$ (numerical)
Number field:  4.0.9889088.1
Galois group:  $D_{4}$
Jacobians:  22

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 22 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3710 28040180 151506015710 806577460110800 4297589667109673550 22901971102896752866580 122044987209661020582348110 650377909082734741819431449600 3465863769220620080447450852778830 18469587807040194426047738657665122900

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 48 5262 389460 28402374 2073054148 151333717854 11047396090464 806460128182206 58871587518022080 4297625837825484382

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.9889088.1.
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.ba_ls$2$(not in LMFDB)