Properties

 Label 3.7.aj_bn_aen 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: $1 - 9 x + 39 x^{2} - 117 x^{3} + 273 x^{4} - 441 x^{5} + 343 x^{6}$ Frobenius angles: $\pm0.0498744256324$, $\pm0.209638042653$, $\pm0.524777204314$ Angle rank: $3$ (numerical) Number field: 6.0.1305639.1 Galois group: $A_4\times C_2$

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 $A(\F_{q^r})$ 89 108847 37405187 13339526391 4796042024159 1637863504126903 557473962960800576 191317740292278438471 65702998610871049393937 22538679394105663381021087

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 47 317 2315 16979 118331 821960 5756867 40347857 282466967

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The endomorphism algebra of this simple isogeny class is 6.0.1305639.1.
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.j_bn_en $2$ (not in LMFDB)