Properties

Label 2.41.av_hf
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:  $1 - 21 x + 187 x^{2} - 861 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.0153876165359$, $\pm0.278522863005$
Angle rank:  $2$ (numerical)
Number field:  4.0.16317.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 987 2715237 4745662803 7984493803125 13421063357891952 22562527591813070925 37928895301445060277267 63758955100453314303853125 107178920473686561823608718083 180167782631303010314312004218112

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 21 1615 68859 2825611 115842426 4749901567 194752569711 7984915734451 327381902340129 13422659285930830

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.16317.1.
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.v_hf$2$(not in LMFDB)