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

• Label: 2.73.aba_lr
• 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:	$1 - 26 x + 303 x^{2} - 1898 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.0862798287125$, $\pm0.311551167525$
Angle rank:	$2$ (numerical)
Number field:	4.0.606096.2
Galois group:	$D_{4}$
Jacobians:	$24$
Isomorphism classes:	24

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3709$	$28028913$	$151475560000$	$806535138842169$	$4297551398461044229$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$48$	$5260$	$389382$	$28400884$	$2073035688$	$151333556110$	$11047395048696$	$806460122499364$	$58871587474878486$	$4297625837346598300$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=72x^6+31x^5+12x^4+42x^3+69x^2+25x+62$
• $y^2=53x^6+14x^5+14x^4+52x^3+42x^2+47x+17$
• $y^2=11x^6+28x^5+2x^4+41x^3+2x^2+9x+43$
• $y^2=58x^6+4x^5+69x^4+60x^3+26x^2+71x+69$
• $y^2=34x^6+17x^5+9x^4+54x^3+24x^2+2x+32$
• $y^2=59x^6+31x^5+33x^4+7x^3+29x^2+43x+29$
• $y^2=15x^6+36x^5+37x^4+11x^3+43x^2+28x+6$
• $y^2=48x^6+52x^5+66x^4+21x^3+48x+29$
• $y^2=16x^6+28x^5+7x^4+32x^3+42x^2+62x+37$
• $y^2=70x^6+20x^5+34x^4+65x^3+61x^2+70x+59$
• $y^2=6x^6+60x^5+13x^4+40x^3+59x^2+17x+68$
• $y^2=12x^6+67x^5+9x^4+24x^3+8x^2+13x+53$
• $y^2=70x^6+60x^5+14x^4+2x^3+39x^2+45x+10$
• $y^2=51x^6+62x^5+23x^4+21x^3+24x^2+22x+67$
• $y^2=66x^6+37x^5+7x^4+17x^3+47x^2+9x+41$
• $y^2=15x^6+22x^5+37x^4+57x^3+70x^2+23x+42$
• $y^2=72x^6+43x^5+36x^4+24x^3+41x^2+25x+68$
• $y^2=44x^6+45x^5+67x^4+70x^3+60x^2+38x+34$
• $y^2=x^6+52x^5+7x^4+9x^3+71x^2+58x+52$
• $y^2=31x^6+57x^5+47x^4+19x^3+30x^2+61x+35$
• $y^2=33x^6+56x^5+65x^4+64x^3+29x^2+24x+22$
• $y^2=50x^6+19x^5+45x^4+38x^3+20x^2+67x+14$
• $y^2=20x^6+37x^5+61x^4+49x^3+63x^2+18x+48$
• $y^2=61x^6+42x^5+67x^4+67x^3+10x^2+4x+6$

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 4.0.606096.2.

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.ba_lr	$2$	(not in LMFDB)