Properties

Label 2.73.aba_lu
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:  $( 1 - 16 x + 73 x^{2} )( 1 - 10 x + 73 x^{2} )$
Frobenius angles:  $\pm0.114200251220$, $\pm0.301013746420$
Angle rank:  $2$ (numerical)
Jacobians:  66

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 66 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3712 28062720 151566932608 806661763891200 4297664587820870272 22902016191270812144640 122045004050655148160499328 650377910905101662103797760000 3465863767456453371048559807829632 18469587806019406883725623126076953600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 48 5266 389616 28405342 2073090288 151334015794 11047397614896 806460130441918 58871587488055728 4297625837587960786

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.aq $\times$ 1.73.ak 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_ao$2$(not in LMFDB)
2.73.g_ao$2$(not in LMFDB)
2.73.ba_lu$2$(not in LMFDB)
2.73.ax_jy$3$(not in LMFDB)
2.73.b_aew$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ag_ao$2$(not in LMFDB)
2.73.g_ao$2$(not in LMFDB)
2.73.ba_lu$2$(not in LMFDB)
2.73.ax_jy$3$(not in LMFDB)
2.73.b_aew$3$(not in LMFDB)
2.73.aq_hy$4$(not in LMFDB)
2.73.ae_di$4$(not in LMFDB)
2.73.e_di$4$(not in LMFDB)
2.73.q_hy$4$(not in LMFDB)
2.73.abh_qc$6$(not in LMFDB)
2.73.aj_bi$6$(not in LMFDB)
2.73.ab_aew$6$(not in LMFDB)
2.73.j_bi$6$(not in LMFDB)
2.73.x_jy$6$(not in LMFDB)
2.73.bh_qc$6$(not in LMFDB)
2.73.ax_jo$12$(not in LMFDB)
2.73.an_hg$12$(not in LMFDB)
2.73.al_bs$12$(not in LMFDB)
2.73.ab_ea$12$(not in LMFDB)
2.73.b_ea$12$(not in LMFDB)
2.73.l_bs$12$(not in LMFDB)
2.73.n_hg$12$(not in LMFDB)
2.73.x_jo$12$(not in LMFDB)