Properties

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

This isogeny class is simple and geometrically 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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3655 27964405 151555075735 806750293259925 4297777185989508400 22902083003160702277405 122045011513001851447160695 650377886807856942720105502725 3465863743574124172417534602468655 18469587796287264700614835135758726400

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

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.3128013.1.
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.bb_ml$2$(not in LMFDB)