Properties

Label 2.73.abf_ov
Base Field $\F_{73}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $1 - 31 x + 385 x^{2} - 2263 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0748266886772$, $\pm0.181589986389$
Angle rank:  $2$ (numerical)
Number field:  4.0.33725.1
Galois group:  $D_{4}$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3421 27398789 151033349269 806479216997861 4297734053417660416 22902142363183930989461 122045067892049379349894501 650377900560688287723042728069 3465863724656704319612486448962941 18469587769745547144171578195578650624

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 43 5139 388243 28398915 2073123798 151334849523 11047403393755 806460117614979 58871586761053939 4297625829147519214

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.33725.1.
All geometric endomorphisms are defined over $\F_{73}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.bf_ov$2$(not in LMFDB)