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

• Label: 2.73.aba_lu
• Base field: $\F_{73}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{73}$
Dimension:	$2$
L-polynomial:	$( 1 - 16 x + 73 x^{2} )( 1 - 10 x + 73 x^{2} )$
	$1 - 26 x + 306 x^{2} - 1898 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.114200251220$, $\pm0.301013746420$
Angle rank:	$2$ (numerical)
Jacobians:	$66$
Isomorphism classes:	382

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3712$	$28062720$	$151566932608$	$806661763891200$	$4297664587820870272$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$48$	$5266$	$389616$	$28405342$	$2073090288$	$151334015794$	$11047397614896$	$806460130441918$	$58871587488055728$	$4297625837587960786$

Jacobians and polarizations

This isogeny class contains the Jacobians of 66 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=5x^6+25x^5+4x^4+66x^3+15x^2+14x+38$
• $y^2=13x^6+52x^5+53x^4+10x^3+x^2+29x+58$
• $y^2=44x^6+6x^5+44x^4+20x^3+66x^2+50x+39$
• $y^2=44x^6+63x^5+53x^4+14x^3+24x^2+7x+14$
• $y^2=17x^6+17x^5+58x^4+45x^3+21x^2+45x+10$
• $y^2=50x^6+5x^5+19x^4+43x^3+19x^2+5x+50$
• $y^2=5x^6+3x^5+67x^4+70x^3+3x^2+72x+7$
• $y^2=29x^6+53x^5+46x^4+70x^3+44x^2+7x+6$
• $y^2=50x^6+27x^5+3x^4+27x^3+27x^2+63x+68$
• $y^2=70x^6+3x^5+x^4+28x^3+x^2+62x+30$
• $y^2=25x^6+61x^5+28x^4+60x^3+6x^2+11x+39$
• $y^2=43x^6+18x^5+56x^4+64x^3+40x^2+12x+51$
• $y^2=13x^6+44x^5+7x^4+50x^3+66x^2+35x+66$
• $y^2=44x^6+58x^5+33x^4+23x^3+54x^2+54x+26$
• $y^2=17x^6+61x^5+28x^4+29x^3+47x^2+12x+21$
• $y^2=5x^6+12x^5+54x^4+72x^3+50x^2+14x+49$
• $y^2=6x^6+37x^5+65x^4+49x^3+31x^2+31x+31$
• $y^2=60x^6+33x^5+70x^4+22x^3+23x^2+66x+29$
• $y^2=43x^6+53x^5+71x^4+11x^3+15x^2+30x+58$
• $y^2=40x^6+53x^5+6x^4+60x^3+11x^2+6x+7$
• and

• $y^2=10x^6+44x^5+50x^4+21x^3+56x^2+26x+63$
• $y^2=26x^6+61x^5+53x^4+34x^3+53x^2+61x+26$
• $y^2=11x^6+54x^5+17x^4+55x^3+23x^2+37x+18$
• $y^2=18x^6+42x^5+66x^4+2x^3+27x^2+5x+48$
• $y^2=14x^6+19x^5+6x^4+21x^3+30x^2+32x+5$
• $y^2=29x^6+3x^5+8x^4+46x^3+14x^2+62x+58$
• $y^2=40x^6+55x^5+50x^4+68x^3+46x^2+2x+31$
• $y^2=6x^6+65x^5+7x^4+32x^3+39x^2+35x+42$
• $y^2=20x^6+69x^5+4x^4+5x^3+36x^2+45x+57$
• $y^2=41x^6+66x^5+15x^4+65x^3+61x^2+30x+41$
• $y^2=19x^6+32x^5+65x^4+65x^3+69x^2+8x+48$
• $y^2=45x^6+31x^5+43x^4+48x^3+35x^2+5x+49$
• $y^2=67x^6+5x^5+71x^4+31x^3+59x^2+22x+6$
• $y^2=8x^6+53x^5+29x^4+21x^3+36x^2+57x+53$
• $y^2=44x^6+40x^5+71x^4+13x^3+35x^2+69x+40$
• $y^2=28x^6+48x^5+51x^4+45x^3+21x^2+61x+33$
• $y^2=4x^6+72x^5+61x^4+57x^3+55x^2+43x+31$
• $y^2=40x^6+18x^5+3x^4+58x^3+48x^2+54x+60$
• $y^2=45x^6+15x^5+24x^4+42x^3+4x^2+16x+63$
• $y^2=22x^6+18x^5+47x^4+20x^3+26x^2+18x+51$
• $y^2=69x^6+60x^5+30x^4+59x^3+14x^2+52x+61$
• $y^2=59x^6+45x^5+34x^4+26x^3+65x^2+13x+7$
• $y^2=59x^6+66x^5+41x^4+18x^3+23x^2+10x+13$
• $y^2=51x^6+68x^5+70x^4+5x^3+70x^2+68x+51$
• $y^2=4x^6+40x^5+63x^4+71x^3+34x^2+10x+60$
• $y^2=15x^6+21x^5+54x^4+43x^3+31x^2+50x+44$
• $y^2=45x^6+26x^5+43x^4+37x^3+37x^2+22x+25$
• $y^2=20x^6+13x^5+63x^4+66x^3+63x^2+13x+20$
• $y^2=16x^6+14x^5+20x^4+28x^3+23x^2+50$
• $y^2=7x^6+24x^5+61x^4+43x^3+6x^2+6x+63$
• $y^2=29x^6+12x^5+35x^4+42x^3+35x^2+12x+29$
• $y^2=20x^6+20x^5+15x^4+59x^3+15x^2+20x+20$
• $y^2=9x^6+70x^5+2x^4+36x^3+53x^2+45x+14$
• $y^2=46x^6+16x^5+53x^4+41x^3+27x^2+21x+66$
• $y^2=7x^6+20x^5+13x^4+57x^3+37x^2+11x+31$
• $y^2=46x^6+24x^5+x^4+2x^3+32x^2+48x+24$
• $y^2=2x^6+68x^5+69x^4+20x^3+62x^2+33x+8$
• $y^2=34x^6+27x^5+46x^4+17x^3+21x^2+34x+33$
• $y^2=13x^6+16x^5+60x^4+47x^3+47x^2+55x+20$
• $y^2=63x^6+28x^5+20x^4+32x^3+58x^2+70x+11$
• $y^2=34x^6+14x^5+30x^4+25x^3+12x^2+6x+47$
• $y^2=65x^6+3x^5+7x^4+24x^3+7x^2+3x+65$
• $y^2=10x^6+61x^5+65x^4+11x^3+65x^2+61x+10$
• $y^2=7x^6+20x^5+44x^4+52x^3+71x^2+38x+31$
• $y^2=34x^6+29x^5+55x^4+62x^3+55x^2+29x+34$
• $y^2=30x^6+22x^5+67x^4+39x^3+67x^2+22x+30$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{73}$.

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.aq $\times$ 1.73.ak and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.73.aq : \(\Q(\sqrt{-1}) \).
• 1.73.ak : \(\Q(\sqrt{-3}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.73.ag_ao	$2$	(not in LMFDB)
2.73.g_ao	$2$	(not in LMFDB)
2.73.ba_lu	$2$	(not in LMFDB)
2.73.ax_jy	$3$	(not in LMFDB)
2.73.b_aew	$3$	(not in LMFDB)