Properties

Label 2.41.ay_is
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:  $( 1 - 12 x + 41 x^{2} )^{2}$
Frobenius angles:  $\pm0.113551764296$, $\pm0.113551764296$
Angle rank:  $1$ (numerical)
Jacobians:  3

This isogeny class is not 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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 900 2624400 4715568900 7982207078400 13423713390562500 22564196541890816400 37929502028360121480900 63759117458480055518822400 107178954605339646251452752900 180167788621537529528113580250000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 18 1558 68418 2824798 115865298 4750252918 194755685058 7984936067518 327382006596498 13422659732208598

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The isogeny class factors as 1.41.am 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-5}) \)$)$
All geometric endomorphisms are defined over $\F_{41}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.41.a_ack$2$(not in LMFDB)
2.41.y_is$2$(not in LMFDB)
2.41.m_dz$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.41.a_ack$2$(not in LMFDB)
2.41.y_is$2$(not in LMFDB)
2.41.m_dz$3$(not in LMFDB)
2.41.a_ck$4$(not in LMFDB)
2.41.am_dz$6$(not in LMFDB)