# Properties

 Label 3.5.ah_bc_acx Base Field $\F_{5}$ Dimension $3$ $p$-rank $2$ Does not contain a Jacobian

# Learn more about

## Invariants

 Base field: $\F_{5}$ Dimension: $3$ Weil polynomial: $1 - 7 x + 28 x^{2} - 75 x^{3} + 140 x^{4} - 175 x^{5} + 125 x^{6}$ Frobenius angles: $\pm0.117658111351$, $\pm0.327130732663$, $\pm0.462990021908$ Angle rank: $3$ (numerical) Number field: 6.0.16537520.2 Galois group: The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

## Newton polygon

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

## 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 $A(\F_{q^r})$ 37 20387 2300068 236346491 29793108217 3837497853104 480136763602757 59746888106691803 7462330081330354804 932458842786590399507

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 33 146 605 3049 15720 78665 391557 1956206 9777533

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.