Properties

Label 2.73.abb_mg
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:  $1 - 27 x + 318 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0678243041225$, $\pm0.294103344880$
Angle rank:  $2$ (numerical)
Number field:  4.0.4081468.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3650 27907900 151396860800 806518216312000 4297551893233813250 22901927122400295654400 122044936033351003934128850 650377865497401558554118624000 3465863743985487393499327596694400 18469587799113378182734745643655109500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 47 5237 389180 28400289 2073035927 151333427234 11047391458031 806460074136961 58871587089375020 4297625835981020357

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.4081468.1.
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.bb_mg$2$(not in LMFDB)