Properties

Label 2.73.abb_mq
Base Field $\F_{73}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $( 1 - 14 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$
Frobenius angles:  $\pm0.194368965322$, $\pm0.224822766824$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3660 28020960 151713339120 806979549974400 4297988490122748300 22902203903730989967360 122045028321101009140057740 650377835013597824624209804800 3465863672899846277724153175557360 18469587741925119242937477426782776800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 47 5257 389990 28416529 2073246527 151335256174 11047399811831 806460036337441 58871585881905590 4297625822674078057

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ao $\times$ 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.ab_abk$2$(not in LMFDB)
2.73.b_abk$2$(not in LMFDB)
2.73.bb_mq$2$(not in LMFDB)