Properties

Label 2.73.abb_mp
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:  $1 - 27 x + 327 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.173277117652$, $\pm0.242024654440$
Angle rank:  $2$ (numerical)
Number field:  4.0.271525.1
Galois group:  $D_{4}$
Jacobians:  11

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 11 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3659 28009645 151681682531 806933924203525 4297947348358642544 22902182511126297563605 122045029578036363197126411 650377850957442934946528271525 3465863692034119534228136090726459 18469587755817715140672946250406688000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 47 5255 389909 28414923 2073226682 151335114815 11047399925609 806460056107603 58871586206922707 4297625825906699150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.271525.1.
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_mp$2$(not in LMFDB)