Properties

Label 2.173.abu_bhn
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 173 x^{2} )( 1 - 21 x + 173 x^{2} )$
Frobenius angles:  $\pm0.100717649571$, $\pm0.205732831898$
Angle rank:  $2$ (numerical)
Jacobians:  42

This isogeny class is not 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 42 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22797 884637585 26803519496208 802388604578081625 24013930738364481950397 718709550259888705123307520 21510249796945308659028315026373 643780251826900989334563911164115625 19267699140912511004343907100983319248272 576662967582237714701138078621429197939645425

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29556 5176706 895777892 154964685088 26808764337414 4637914433706976 802359179151689668 138808137877868610698 24013807852615882117236

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.az $\times$ 1.173.av and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{173}$.

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.ae_agx$2$(not in LMFDB)
2.173.e_agx$2$(not in LMFDB)
2.173.bu_bhn$2$(not in LMFDB)