Properties

Label 2.73.abc_mx
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:  $1 - 28 x + 335 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0725767491279$, $\pm0.268662818956$
Angle rank:  $2$ (numerical)
Number field:  4.0.1907472.4
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3593 27799041 151355800484 806569187104521 4297636222448107673 22901983765503633946512 122044947558865405889598569 650377850437167688706024041353 3465863727492030544718483963950628 18469587793598918013047812058400076641

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5216 389074 28402084 2073076606 151333801526 11047392501310 806460055462468 58871586809215138 4297625834697879296

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.1907472.4.
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.bc_mx$2$(not in LMFDB)