Properties

Label 2.73.abc_nd
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:  $( 1 - 15 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$
Frobenius angles:  $\pm0.159004799845$, $\pm0.224822766824$
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
$A(\F_{q^r})$ 3599 27867057 151552795904 806873274258489 4297951420023512999 22902218368895659032576 122045066030539993364569127 650377872951958257524086538025 3465863699198358666291218914893056 18469587754491797515450339119962847777

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5228 389578 28412788 2073228646 151335351758 11047403225254 806460083380516 58871586328615354 4297625825598175868

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ap $\times$ 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ac_abx$2$(not in LMFDB)
2.73.c_abx$2$(not in LMFDB)
2.73.bc_nd$2$(not in LMFDB)