Properties

 Label 5.3.al_cj_ain_wh_absc Base Field $\F_{3}$ Dimension $5$ $p$-rank $3$ Does not contain a Jacobian

Invariants

 Base field: $\F_{3}$ Dimension: $5$ Weil polynomial: $(1-2x+3x^{2})(1-3x+3x^{2})^{2}(1-3x+7x^{2}-9x^{3}+9x^{4})$ Frobenius angles: $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.227267020856$, $\pm0.304086723985$, $\pm0.464830336654$ Angle rank: $3$ (numerical)

Newton polygon

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 10 85260 31430560 5187218400 1101908764000 244394982558720 52712767854495010 11956788913150972800 2906332605830394821920 716644154693490866304000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -7 11 47 115 308 857 2303 6451 19361 58946

Decomposition

1.3.ad 2 $\times$ 1.3.ac $\times$ 2.3.ad_h

Base change

This is a primitive isogeny class.