Properties

Label 2.113.abj_tz
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 35 x + 519 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0338691187123$, $\pm0.273965054653$
Angle rank:  $2$ (numerical)
Number field:  4.0.3721925.1
Galois group:  $C_4$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9299 160677421 2081596484051 26584625768358821 339454417535489545264 4334515652801270765071621 55347513182994454725101116811 706732539822785125234621810213925 9024267958055401135225644097329609539 115230877649715360789030727424741616061696

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12583 1442653 163048491 18424225794 2081948175487 235260495833113 26584441445435283 3004041935616499339 339456738999532863678

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.3721925.1.
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

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