Properties

Label 2.73.abb_mn
Base field $\F_{73}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $1 - 27 x + 325 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.146798730614$, $\pm0.260008220746$
Angle rank:  $2$ (numerical)
Number field:  4.0.1516437.3
Galois group:  $D_{4}$
Jacobians:  $16$
Isomorphism classes:  16

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $3657$ $27987021$ $151618375233$ $806842334319381$ $4297863386245838592$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $47$ $5251$ $389747$ $28411699$ $2073186182$ $151334804491$ $11047399528331$ $806460085368643$ $58871586733075055$ $4297625831402083246$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{73}$.

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.1516437.3.

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.bb_mn$2$(not in LMFDB)