# Properties

 Label 4.2.ae_e_h_av Base Field $\F_{2}$ Dimension $4$ $p$-rank $4$ Does not contain a Jacobian

## Invariants

 Base field: $\F_{2}$ Dimension: $4$ Weil polynomial: $1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8}$ Frobenius angles: $\pm0.0764513550391$, $\pm0.143118021706$, $\pm0.323548644961$, $\pm0.943118021706$ Angle rank: $1$ (numerical) Number field: $$\Q(\zeta_{15})$$ Galois group: $C_4\times C_2$

This isogeny class is simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $4$ Slopes: $[0, 0, 0, 0, 1, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 1 31 7471 55831 1343281 14127661 308739901 5138741071 82847868931 1240548212401

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 -3 14 13 39 54 146 301 608 1147

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.