Properties

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

Learn more about

Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $( 1 - 16 x + 73 x^{2} )( 1 - 11 x + 73 x^{2} )$
Frobenius angles:  $\pm0.114200251220$, $\pm0.277387524567$
Angle rank:  $2$ (numerical)
Jacobians:  25

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 25 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3654 27953100 151523428896 806704103520000 4297733246546141094 22902054632694247046400 122045001160908380902872966 650377888569925802158965120000 3465863749693557010910075592093984 18469587801718243842065602839755527500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 47 5245 389504 28406833 2073123407 151334269810 11047397353319 806460102746593 58871587186332992 4297625836587137725

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.aq $\times$ 1.73.al 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.af_abe$2$(not in LMFDB)
2.73.f_abe$2$(not in LMFDB)
2.73.bb_mk$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.af_abe$2$(not in LMFDB)
2.73.f_abe$2$(not in LMFDB)
2.73.bb_mk$2$(not in LMFDB)
2.73.ar_ie$4$(not in LMFDB)
2.73.af_dc$4$(not in LMFDB)
2.73.f_dc$4$(not in LMFDB)
2.73.r_ie$4$(not in LMFDB)