Properties

Label 2.73.abd_nq
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:  $( 1 - 16 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$
Frobenius angles:  $\pm0.114200251220$, $\pm0.224822766824$
Angle rank:  $2$ (numerical)
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3538 27702540 151357182568 806706829612800 4297842204101706898 22902166557382887440640 122045056505728396588624114 650377887008980252465363737600 3465863721517396143177775493349352 18469587775540279050114349873794770700

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 45 5197 389076 28406929 2073175965 151335009394 11047402363077 806460100811041 58871586707729268 4297625830495875757

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.aq $\times$ 1.73.an 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.ad_ack$2$(not in LMFDB)
2.73.d_ack$2$(not in LMFDB)
2.73.bd_nq$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ad_ack$2$(not in LMFDB)
2.73.d_ack$2$(not in LMFDB)
2.73.bd_nq$2$(not in LMFDB)
2.73.at_iq$4$(not in LMFDB)
2.73.ah_cq$4$(not in LMFDB)
2.73.h_cq$4$(not in LMFDB)
2.73.t_iq$4$(not in LMFDB)