Properties

 Label 3.23.aw_ip_abzv Base Field $\F_{23}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes

Learn more about

Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $1 - 22 x + 223 x^{2} - 1347 x^{3} + 5129 x^{4} - 11638 x^{5} + 12167 x^{6}$ Frobenius angles: $\pm0.0394215835568$, $\pm0.175002735951$, $\pm0.351893565228$ Angle rank: $3$ (numerical) Number field: 6.0.1392115799.1 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 it is unknown whether it contains a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4513 137768351 1805348874844 21914201142006719 266505266925446872048 3243783930808944944698928 39471581442512643698256350471 480252812996839244202985639633775 5843212712169828261728714380882050364 71094324648032871498566508650751646712576

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 492 12197 279836 6433207 148019145 3404825216 78311319396 1801153175195 41426497145507

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The endomorphism algebra of this simple isogeny class is 6.0.1392115799.1.
All geometric endomorphisms are defined over $\F_{23}$.

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 3.23.w_ip_bzv $2$ (not in LMFDB)