Properties

Label 2.73.abc_na
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:  $( 1 - 16 x + 73 x^{2} )( 1 - 12 x + 73 x^{2} )$
Frobenius angles:  $\pm0.114200251220$, $\pm0.252180272892$
Angle rank:  $2$ (numerical)
Jacobians:  20

This isogeny class is not 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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3596 27833040 151454289068 806721737932800 4297796432309223596 22902107915204516690640 122045019013413640032761612 650377878209633108279564697600 3465863731090637397489247831019852 18469587789429404773790391526386133200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5222 389326 28407454 2073153886 151334621894 11047398969310 806460089899966 58871586870341518 4297625833727689382

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.aq $\times$ 1.73.am and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{73}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ae_abu$2$(not in LMFDB)
2.73.e_abu$2$(not in LMFDB)
2.73.bc_na$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ae_abu$2$(not in LMFDB)
2.73.e_abu$2$(not in LMFDB)
2.73.bc_na$2$(not in LMFDB)
2.73.as_ik$4$(not in LMFDB)
2.73.ag_cw$4$(not in LMFDB)
2.73.g_cw$4$(not in LMFDB)
2.73.s_ik$4$(not in LMFDB)