Properties

Label 2.73.abd_np
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:  $1 - 29 x + 353 x^{2} - 2117 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0968714105366$, $\pm0.233378984548$
Angle rank:  $2$ (numerical)
Number field:  4.0.64389.1
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
$A(\F_{q^r})$ 3537 27691173 151323163281 806651429180229 4297779978808514832 22902114056559515072325 122045023081690245757907073 650377872779361553918863042309 3465863720674379127983198581237089 18469587780980620353167465441617072128

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 45 5195 388989 28404979 2073145950 151334662475 11047399337565 806460083166499 58871586693409677 4297625831761770350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.64389.1.
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_np$2$(not in LMFDB)