Properties

Label 2.49.aba_kg
Base Field $\F_{7^{2}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{7^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x )^{2}( 1 - 12 x + 49 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.172237328522$
Angle rank:  $1$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1368 5428224 13765025304 33220730880000 79791377171274648 191581213414880572416 459986311377939489737688 1104427434481769406136320000 2651730693820135298968313081304 6366805686837945423778583458427904

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 24 2258 117000 5762686 282472104 13841285906 678222740856 33232923355006 1628413504543800 79792265369312978

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
The isogeny class factors as 1.49.ao $\times$ 1.49.am and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{7^{2}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.49.ac_acs$2$(not in LMFDB)
2.49.c_acs$2$(not in LMFDB)
2.49.ba_kg$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.49.ac_acs$2$(not in LMFDB)
2.49.c_acs$2$(not in LMFDB)
2.49.ba_kg$2$(not in LMFDB)
2.49.am_du$4$(not in LMFDB)
2.49.m_du$4$(not in LMFDB)