# Properties

 Label 4.2.ad_c_a_b Base field $\F_{2}$ Dimension $4$ $p$-rank $4$ Ordinary yes Supersingular no Simple yes Geometrically simple no Primitive yes Principally polarizable yes

## Invariants

 Base field: $\F_{2}$ Dimension: $4$ L-polynomial: $1 - 3 x + 2 x^{2} + x^{4} + 8 x^{6} - 24 x^{7} + 16 x^{8}$ Frobenius angles: $\pm0.0298810195513$, $\pm0.106143893905$, $\pm0.506143893905$, $\pm0.829881019551$ Angle rank: $2$ (numerical) Number field: 8.0.26265625.1 Galois group: $C_2^2:C_4$

This isogeny class is simple but not geometrically simple.

## Newton polygon

This isogeny class is ordinary. $p$-rank: $4$ Slopes: $[0, 0, 0, 0, 1, 1, 1, 1]$

## Point counts

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $1$ $55$ $1621$ $27775$ $609961$

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $0$ $0$ $0$ $4$ $15$ $90$ $105$ $244$ $540$ $1075$

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
 The endomorphism algebra of this simple isogeny class is 8.0.26265625.1.
Endomorphism algebra over $\overline{\F}_{2}$
 The base change of $A$ to $\F_{2^{5}}$ is 2.32.aj_cb 2 and its endomorphism algebra is $\mathrm{M}_{2}($4.0.1025.1$)$
All geometric endomorphisms are defined over $\F_{2^{5}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
TwistExtension degreeCommon base change
4.2.d_c_a_b$2$4.4.af_g_u_adb
4.2.c_c_f_l$5$(not in LMFDB)
4.2.c_h_k_v$5$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension degreeCommon base change
4.2.d_c_a_b$2$4.4.af_g_u_adb
4.2.c_c_f_l$5$(not in LMFDB)
4.2.c_h_k_v$5$(not in LMFDB)
4.2.ac_c_af_l$10$(not in LMFDB)
4.2.ac_h_ak_v$10$(not in LMFDB)
4.2.a_f_a_n$10$(not in LMFDB)
4.2.ab_ac_b_d$15$(not in LMFDB)
4.2.a_af_a_n$20$(not in LMFDB)
4.2.b_ac_ab_d$30$(not in LMFDB)