Properties

Label 2.73.abd_nn
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:  $1 - 29 x + 351 x^{2} - 2117 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0594050003777$, $\pm0.246672053911$
Angle rank:  $2$ (numerical)
Number field:  4.0.633717.2
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3535 27668445 151255131055 806540290412325 4297653725432762800 22902004103705763532965 122044946854988994504068695 650377830614520731227512433125 3465863702642696864309784740170015 18469587775464170380618728654228921600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 45 5191 388815 28401067 2073085050 151333935919 11047392437595 806460030882643 58871586387121305 4297625830478166286

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.633717.2.
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.bd_nn$2$(not in LMFDB)