Properties

 Label 3.7.ak_bz_agk Base Field $\F_{7}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{7}$ Dimension: $3$ L-polynomial: $1 - 10 x + 51 x^{2} - 166 x^{3} + 357 x^{4} - 490 x^{5} + 343 x^{6}$ Frobenius angles: $\pm0.0683199847700$, $\pm0.284796870547$, $\pm0.407332955184$ Angle rank: $3$ (numerical) Number field: 6.0.12178624.1 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 does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 86 121948 44162978 13762075696 4658150804726 1618368845763772 558329821626191666 191611914119074964224 65713443926415447470702 22540570795576448403639388

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 52 376 2388 16488 116920 823226 5765724 40354270 282490672

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The endomorphism algebra of this simple isogeny class is 6.0.12178624.1.
All geometric endomorphisms are defined over $\F_{7}$.

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 3.7.k_bz_gk $2$ (not in LMFDB)