Properties

Label 5.2.ah_z_ach_ec_age
Base Field $\F_{2}$
Dimension $5$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.105278500939$, $\pm0.25$, $\pm0.25$, $\pm0.316838792568$, $\pm0.641249159631$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2 2300 51038 3910000 72017402 763018100 26336547722 1076814000000 34196345458262 1244370684807500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 6 14 38 56 42 94 254 500 1126

Decomposition

1.2.ac 2 $\times$ 3.2.ad_f_ah

Base change

This is a primitive isogeny class.