Properties

Label 2.41.as_ga
Base Field $\F_{41}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{41}$
Dimension:  $2$
L-polynomial:  $1 - 18 x + 156 x^{2} - 738 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.136556295479$, $\pm0.334734336659$
Angle rank:  $2$ (numerical)
Number field:  4.0.2750272.1
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1082 2806708 4776217418 7990910985808 13422719888173082 22563387862602739348 37929316120910038511978 63759098076945360956347392 107178951716386911480770805098 180167785666375184195028472013908

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 24 1670 69300 2827878 115856724 4750082678 194754730488 7984933640254 327381997772088 13422659512046390

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.2750272.1.
All geometric endomorphisms are defined over $\F_{41}$.

Base change

This is a primitive isogeny class.

Twists

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