Properties

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

Learn more about

Invariants

Base field:  $\F_{41}$
Dimension:  $2$
L-polynomial:  $1 - 21 x + 191 x^{2} - 861 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.138203224180$, $\pm0.238302673482$
Angle rank:  $2$ (numerical)
Number field:  4.0.55125.1
Galois group:  $C_4$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 991 2730205 4763222671 7995899509605 13426124321479216 22564196278680584005 37929311564218773696631 63759030388920630320850405 107178928861980900446883344911 180167782965483875237718100000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 21 1623 69111 2829643 115886106 4750252863 194754707091 7984925163283 327381927962481 13422659310827598

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.55125.1.
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_hj$2$(not in LMFDB)