Properties

Label 2.73.abc_mv
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:  $( 1 - 17 x + 73 x^{2} )( 1 - 11 x + 73 x^{2} )$
Frobenius angles:  $\pm0.0323195869136$, $\pm0.277387524567$
Angle rank:  $2$ (numerical)
Jacobians:  13

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 13 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3591 27776385 151290151488 806466922832025 4297526514615651471 22901893365903937781760 122044886172924763129313967 650377812936621009927456376425 3465863703786211109133699353458752 18469587776247426631825842836030449425

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5212 388906 28398484 2073023686 151333204174 11047386944710 806460008962276 58871586406545178 4297625830660419532

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ar $\times$ 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.ag_abp$2$(not in LMFDB)
2.73.g_abp$2$(not in LMFDB)
2.73.bc_mv$2$(not in LMFDB)
2.73.ae_cr$3$(not in LMFDB)
2.73.ab_bk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ag_abp$2$(not in LMFDB)
2.73.g_abp$2$(not in LMFDB)
2.73.bc_mv$2$(not in LMFDB)
2.73.ae_cr$3$(not in LMFDB)
2.73.ab_bk$3$(not in LMFDB)
2.73.av_jw$6$(not in LMFDB)
2.73.as_ip$6$(not in LMFDB)
2.73.b_bk$6$(not in LMFDB)
2.73.e_cr$6$(not in LMFDB)
2.73.s_ip$6$(not in LMFDB)
2.73.v_jw$6$(not in LMFDB)