Abelian variety isogeny class 2.73.x_kr over $\F_{73}$

• Label: 2.73.x_kr
• 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

Invariants

Base field:	$\F_{73}$
Dimension:	$2$
L-polynomial:	$1 + 23 x + 277 x^{2} + 1679 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.707851015916$, $\pm0.764425206862$
Angle rank:	$2$ (numerical)
Number field:	4.0.611525.2
Galois group:	$D_{4}$
Jacobians:	$20$
Isomorphism classes:	20

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7309$	$28541645$	$150593239981$	$807019150913525$	$4297442550308814544$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$97$	$5355$	$387109$	$28417923$	$2072983182$	$151333880115$	$11047408099909$	$806460010989603$	$58871586967561657$	$4297625831908927150$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which all are hyperelliptic):

• $y^2=46 x^6+31 x^5+62 x^4+70 x^3+72 x^2+41 x+62$
• $y^2=28 x^6+48 x^5+10 x^4+11 x^3+31 x^2+2 x+27$
• $y^2=64 x^6+16 x^5+45 x^4+65 x^3+49 x^2+41 x+4$
• $y^2=5 x^6+33 x^5+45 x^4+64 x^3+11 x^2+43 x+24$
• $y^2=23 x^6+61 x^5+31 x^4+51 x^3+38 x^2+49 x+19$
• $y^2=41 x^6+60 x^5+27 x^4+24 x^3+66 x^2+63 x+17$
• $y^2=6 x^6+56 x^5+65 x^4+58 x^3+10 x^2+55 x+50$
• $y^2=50 x^6+14 x^5+10 x^4+22 x^3+16 x^2+34 x+67$
• $y^2=52 x^6+27 x^5+55 x^4+31 x^3+14 x^2+68 x+55$
• $y^2=8 x^6+43 x^5+13 x^4+64 x^3+11 x^2+45 x$
• $y^2=67 x^6+22 x^5+39 x^4+18 x^3+27 x^2+66 x+21$
• $y^2=61 x^6+52 x^5+4 x^4+67 x^3+54 x^2+58 x+26$
• $y^2=38 x^6+38 x^5+5 x^4+65 x^3+57 x^2+14 x+19$
• $y^2=16 x^6+52 x^5+8 x^4+13 x^3+12 x^2+34 x+55$
• $y^2=2 x^6+4 x^5+44 x^4+29 x^3+64 x+67$
• $y^2=39 x^6+10 x^5+3 x^4+67 x^3+19 x^2+72 x+64$
• $y^2=67 x^6+42 x^5+56 x^4+4 x^3+60 x^2+38 x+55$
• $y^2=x^6+12 x^5+41 x^4+56 x^3+4 x^2+63 x+4$
• $y^2=33 x^6+32 x^5+44 x^4+43 x^3+65 x^2+30 x+72$
• $y^2=4 x^6+30 x^5+8 x^4+2 x^3+62 x^2+9 x+37$

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 4.0.611525.2.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.73.ax_kr	$2$	(not in LMFDB)