Properties

 Label 3.16.ar_ez_axs Base Field $\F_{2^{4}}$ Dimension $3$ Ordinary No $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $( 1 - 4 x )^{2}( 1 - 9 x + 41 x^{2} - 144 x^{3} + 256 x^{4} )$ Frobenius angles: $0$, $0$, $\pm0.0608845495576$, $\pm0.454248801212$ Angle rank: $2$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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 $A(\F_{q^r})$ 1305 14713875 65720368980 275894116999875 1147899425817065625 4720614293017310688000 19341903946139014747337505 79224658626489099271265383875 324514068088727343111863446440180 1329226648038512961508119216076171875

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 226 3915 64226 1044000 16770991 268422840 4294777346 68718526875 1099510512946

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ai $\times$ 2.16.aj_bp and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.16.ai : the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 2.16.aj_bp : 4.0.3625.1.
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 3.16.ab_ap_bo $2$ (not in LMFDB) 3.16.b_ap_abo $2$ (not in LMFDB) 3.16.r_ez_xs $2$ (not in LMFDB) 3.16.af_v_aeu $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.ab_ap_bo $2$ (not in LMFDB) 3.16.b_ap_abo $2$ (not in LMFDB) 3.16.r_ez_xs $2$ (not in LMFDB) 3.16.af_v_aeu $3$ (not in LMFDB) 3.16.aj_cf_alc $4$ (not in LMFDB) 3.16.j_cf_lc $4$ (not in LMFDB) 3.16.an_dp_ark $6$ (not in LMFDB) 3.16.f_v_eu $6$ (not in LMFDB) 3.16.n_dp_rk $6$ (not in LMFDB)