Properties

Label 2.173.abu_bhl
Base field $\F_{173}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

Related objects

Downloads

Learn more

Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $1 - 46 x + 869 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0814447409702$, $\pm0.214601179315$
Angle rank:  $2$ (numerical)
Number field:  4.0.6884928.2
Galois group:  $D_{4}$
Jacobians:  $14$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $22795$ $884514385$ $26802088280620$ $802379675022474025$ $24013891603602758580475$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $128$ $29552$ $5176430$ $895767924$ $154964432548$ $26808759371774$ $4637914355265844$ $802359178169168356$ $138808137869094191750$ $24013807852591803172832$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.6884928.2.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.173.bu_bhl$2$(not in LMFDB)