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

• Label: 2.73.abd_no
• 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:	$1 - 29 x + 352 x^{2} - 2117 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.0792175219317$, $\pm0.240494141700$
Angle rank:	$2$ (numerical)
Number field:	4.0.43928.1
Galois group:	$D_{4}$
Jacobians:	$14$
Isomorphism classes:	14

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3536$	$27679808$	$151289146112$	$806595916116224$	$4297717152587351376$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$45$	$5193$	$388902$	$28403025$	$2073115645$	$151334304654$	$11047396029477$	$806460059878305$	$58871586587305782$	$4297625831777079913$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=46x^6+59x^5+8x^4+58x^3+58x^2+68x+28$
• $y^2=2x^6+27x^5+65x^4+3x^3+63x^2+25x+51$
• $y^2=34x^6+25x^5+27x^4+10x^3+28x+22$
• $y^2=14x^6+38x^5+47x^4+31x^3+54x^2+62x+53$
• $y^2=41x^6+55x^5+16x^4+55x^3+x^2+34x+34$
• $y^2=7x^6+37x^5+65x^4+26x^3+49x^2+41x+61$
• $y^2=31x^6+24x^5+37x^4+7x^3+51x^2+51x+66$
• $y^2=49x^6+18x^5+35x^4+12x^3+13x^2+8x+27$
• $y^2=14x^6+34x^5+15x^4+29x^3+23x^2+14x+59$
• $y^2=5x^6+20x^5+50x^4+72x^3+16x^2+11x+60$
• $y^2=52x^6+51x^5+61x^4+5x^3+42x^2+47$
• $y^2=46x^6+31x^5+14x^4+72x^3+52x^2+41x+58$
• $y^2=62x^6+60x^5+58x^4+57x^3+6x^2+12x+33$
• $y^2=66x^6+2x^4+x^3+51x^2+20x+1$

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 4.0.43928.1.

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.bd_no	$2$	(not in LMFDB)