Properties

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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1 31 7471 55831 1343281 14127661 308739901 5138741071 82847868931 1240548212401

Point counts of the (virtual) curve

$r$ 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.

Additional information

This isogeny class appears as a sporadic example in the classification of abelian varieties with one rational point.