Properties

 Label 3.11.an_dc_amf Base Field $\F_{11}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{11}$ Dimension: $3$ L-polynomial: $1 - 13 x + 80 x^{2} - 317 x^{3} + 880 x^{4} - 1573 x^{5} + 1331 x^{6}$ Frobenius angles: $\pm0.0574705996813$, $\pm0.177271568763$, $\pm0.459404600808$ Angle rank: $3$ (numerical) Number field: 6.0.16537520.2 Galois group: $S_4\times C_2$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

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 $A(\F_{q^r})$ 389 1631855 2310964976 3086263719155 4171462217405179 5570225925550488320 7404286854219691858769 9849201386810600120640395 13109371568696073102909347216 17449351996087422238032233201375

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 113 1304 14397 160829 1774844 19497799 214347317 2357835704 25937349873

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 6.0.16537520.2.
All geometric endomorphisms are defined over $\F_{11}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.11.n_dc_mf $2$ (not in LMFDB)