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

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.

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

 $r$ 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: 1.49.ao : the quaternion algebra over $$\Q$$ ramified at $7$ and $\infty$. 1.49.am : $$\Q(\sqrt{-13})$$.
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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)