Properties

Label 4.2.af_n_az_bn
Base Field $\F_{2}$
Dimension $4$
Ordinary No
$p$-rank $4$
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $4$
Weil polynomial:  $1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8}$
Frobenius angles:  $\pm0.00978468837242$, $\pm0.190215311628$, $\pm0.409784688372$, $\pm0.609784688372$
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
$A(\F_{q^r})$ 1 241 1891 43621 929296 14127661 256112011 4581295525 57170567071 863591055616

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 6 4 10 33 54 124 274 418 781

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.