Properties

Label 2.173.abt_bgh
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:  $1 - 45 x + 839 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0357609426795$, $\pm0.245538694866$
Angle rank:  $2$ (numerical)
Number field:  4.0.8216325.2
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22939 885422461 26802459532471 802364416258161141 24013796695124629472464 718709061642257854338628381 21510248452497837608340592757671 643780248961539014289509727486860325 19267699136381745461919811634671300865899 576662967577860152251679959099022058078935296

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29583 5176503 895750891 154963820094 26808746111367 4637914143825063 802359175580518483 138808137845228121369 24013807852433588560278

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.8216325.2.
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.bt_bgh$2$(not in LMFDB)