Properties

Label 2.73.abd_nr
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:  $1 - 29 x + 355 x^{2} - 2117 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.132995750451$, $\pm0.213626865826$
Angle rank:  $2$ (numerical)
Number field:  4.0.135725.2
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3539 27713909 151391203979 806762117422421 4297903828472423664 22902217410228229672061 122045086821500056528622459 650377896738646028254301466629 3465863717091742380498231724118411 18469587764997079738488286906810017024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 45 5199 389163 28408875 2073205690 151335345423 11047405107231 806460112875699 58871586632554569 4297625828042614414

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.135725.2.
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_nr$2$(not in LMFDB)