Properties

Label 2.73.abb_ml
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:  $1 - 27 x + 323 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.124803810750$, $\pm0.272272309487$
Angle rank:  $2$ (numerical)
Number field:  4.0.3128013.1
Galois group:  $D_{4}$
Jacobians:  $18$
Isomorphism classes:  18

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $3655$ $27964405$ $151555075735$ $806750293259925$ $4297777185989508400$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $47$ $5247$ $389585$ $28408459$ $2073144602$ $151334457279$ $11047398290381$ $806460100561651$ $58871587082387555$ $4297625835323421582$

Jacobians and polarizations

This isogeny class contains the Jacobians of 18 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 4.0.3128013.1.

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_ml$2$(not in LMFDB)