Properties

Label 2.73.abb_me
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:  $( 1 - 17 x + 73 x^{2} )( 1 - 10 x + 73 x^{2} )$
Frobenius angles:  $\pm0.0323195869136$, $\pm0.301013746420$
Angle rank:  $1$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3648 27885312 151333588224 806424595651584 4297457859193040448 22901854924751191474176 122044889062668807734223936 650377835271794272485149798400 3465863721549107233992470829655296 18469587780548589667554266878749226752

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 47 5233 389018 28396993 2072990567 151332950158 11047387206287 806460036657601 58871586708267914 4297625831661242593

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ar $\times$ 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:
Endomorphism algebra over $\overline{\F}_{73}$
The base change of $A$ to $\F_{73^{6}}$ is 1.151334226289.abkhxa 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
All geometric endomorphisms are defined over $\F_{73^{6}}$.
Remainder of endomorphism lattice by field

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.ah_ay$2$(not in LMFDB)
2.73.h_ay$2$(not in LMFDB)
2.73.bb_me$2$(not in LMFDB)
2.73.ay_kf$3$(not in LMFDB)
2.73.ad_cy$3$(not in LMFDB)
2.73.a_afn$3$(not in LMFDB)
2.73.a_bu$3$(not in LMFDB)
2.73.a_dt$3$(not in LMFDB)
2.73.d_cy$3$(not in LMFDB)
2.73.y_kf$3$(not in LMFDB)
2.73.bb_me$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ah_ay$2$(not in LMFDB)
2.73.h_ay$2$(not in LMFDB)
2.73.bb_me$2$(not in LMFDB)
2.73.ay_kf$3$(not in LMFDB)
2.73.ad_cy$3$(not in LMFDB)
2.73.a_afn$3$(not in LMFDB)
2.73.a_bu$3$(not in LMFDB)
2.73.a_dt$3$(not in LMFDB)
2.73.d_cy$3$(not in LMFDB)
2.73.y_kf$3$(not in LMFDB)
2.73.bb_me$3$(not in LMFDB)
2.73.abi_qt$6$(not in LMFDB)
2.73.au_jm$6$(not in LMFDB)
2.73.ar_ii$6$(not in LMFDB)
2.73.ao_hn$6$(not in LMFDB)
2.73.ak_bb$6$(not in LMFDB)
2.73.k_bb$6$(not in LMFDB)
2.73.o_hn$6$(not in LMFDB)
2.73.r_ii$6$(not in LMFDB)
2.73.u_jm$6$(not in LMFDB)
2.73.bi_qt$6$(not in LMFDB)
2.73.a_adt$12$(not in LMFDB)
2.73.a_abu$12$(not in LMFDB)
2.73.a_fn$12$(not in LMFDB)