Properties

Label 2.107.a_ace
Base Field $\F_{107}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
Weil polynomial:  $1-56x^{2}+11449x^{4}$
Frobenius angles:  $\pm0.207861377967$, $\pm0.792138622033$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{30}, \sqrt{-158})\)
Galois group:  $V_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 11394 129823236 1500732099666 17187043241204496 196715135701756650114 2252196834967920957311556 25785341502012774814589422866 295216370445013845652681791897600 3379932275732534789361799747137112194 38696844614160533821108946759223016212996

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 108 11338 1225044 131119126 14025517308 1500733847482 160578147647844 17181861541564318 1838459212420154508 196715135674556767978

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.