# Properties

 Label 2.4.a_ah Base Field $\F_{2^{2}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2^{2}}$ Dimension: $2$ L-polynomial: $1 - 7 x^{2} + 16 x^{4}$ Frobenius angles: $\pm0.0804306232552$, $\pm0.919569376745$ Angle rank: $1$ (numerical) Number field: $$\Q(i, \sqrt{15})$$ Galois group: $C_2^2$ Jacobians: 0

This isogeny class is simple but not geometrically simple.

## Newton polygon

This isogeny class is ordinary.

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

## 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 $A(\F_{q^r})$ 10 100 4090 57600 1050250 16728100 268465690 4324377600 68719562410 1103025062500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 3 65 223 1025 4083 16385 65983 262145 1051923

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{2}}$
 The endomorphism algebra of this simple isogeny class is $$\Q(i, \sqrt{15})$$.
Endomorphism algebra over $\overline{\F}_{2^{2}}$
 The base change of $A$ to $\F_{2^{4}}$ is 1.16.ah 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-15})$$$)$
All geometric endomorphisms are defined over $\F_{2^{4}}$.

## 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 2.4.ac_j $4$ 2.256.abi_bev 2.4.a_h $4$ 2.256.abi_bev 2.4.c_j $4$ 2.256.abi_bev
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.4.ac_j $4$ 2.256.abi_bev 2.4.a_h $4$ 2.256.abi_bev 2.4.c_j $4$ 2.256.abi_bev 2.4.ab_ad $12$ (not in LMFDB) 2.4.b_ad $12$ (not in LMFDB)