Properties

Label 2.139.abq_bbm
Base Field $\F_{139}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $1 - 42 x + 714 x^{2} - 5838 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0544053773055$, $\pm0.207067484893$
Angle rank:  $2$ (numerical)
Number field:  4.0.82000.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14156 366866896 7208152259996 139354860035226880 2692460178339168050396 52020876983675721120755536 1005095197489215896069157964556 19419444495195652481982874540462080 375203088286393051649675575302582389996 7249298871650953099251016125706315696929616

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18986 2683982 373304238 51888998378 7212550514906 1002544355282582 139353666708295198 19370159734131297938 2692452204110027159306

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.82000.1.
All geometric endomorphisms are defined over $\F_{139}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.bq_bbm$2$(not in LMFDB)