Properties

Label 2.73.aba_ln
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:  $( 1 - 17 x + 73 x^{2} )( 1 - 9 x + 73 x^{2} )$
Frobenius angles:  $\pm0.0323195869136$, $\pm0.323434683416$
Angle rank:  $2$ (numerical)
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3705 27983865 151353755280 806364724408425 4297392935156060025 22901835786500290314240 122044908795268953619620105 650377860741637437378296097225 3465863731558385829217058050596240 18469587775942803177444934033898856825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 48 5252 389070 28394884 2072959248 151332823694 11047388992464 806460068239876 58871586878286750 4297625830589537732

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ar $\times$ 1.73.aj 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.ai_ah$2$(not in LMFDB)
2.73.i_ah$2$(not in LMFDB)
2.73.ba_ln$2$(not in LMFDB)
2.73.ac_df$3$(not in LMFDB)
2.73.b_ce$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ai_ah$2$(not in LMFDB)
2.73.i_ah$2$(not in LMFDB)
2.73.ba_ln$2$(not in LMFDB)
2.73.ac_df$3$(not in LMFDB)
2.73.b_ce$3$(not in LMFDB)
2.73.at_jc$6$(not in LMFDB)
2.73.aq_ib$6$(not in LMFDB)
2.73.ab_ce$6$(not in LMFDB)
2.73.c_df$6$(not in LMFDB)
2.73.q_ib$6$(not in LMFDB)
2.73.t_jc$6$(not in LMFDB)