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

• Label: 2.73.abc_ne
• 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:	$( 1 - 14 x + 73 x^{2} )^{2}$
	$1 - 28 x + 342 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.194368965322$, $\pm0.194368965322$
Angle rank:	$1$ (numerical)
Jacobians:	$29$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3600$	$27878400$	$151585635600$	$806923560960000$	$4298001922141290000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$46$	$5230$	$389662$	$28414558$	$2073253006$	$151335574990$	$11047404157822$	$806460072381118$	$58871586023459566$	$4297625821540687150$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 29 curves (of which all are hyperelliptic):

• $y^2=42 x^6+41 x^5+26 x^4+12 x^3+5 x^2+4 x+39$
• $y^2=9 x^6+7 x^5+39 x^4+28 x^3+26 x^2+68 x+27$
• $y^2=28 x^6+46 x^4+46 x^2+28$
• $y^2=52 x^6+x^5+64 x^4+23 x^3+36 x^2+29 x+34$
• $y^2=22 x^6+37 x^5+58 x^4+47 x^3+29 x^2+64 x+21$
• $y^2=34 x^6+57 x^4+57 x^2+34$
• $y^2=15 x^6+53 x^5+22 x^4+51 x^3+68 x^2+5 x+5$
• $y^2=43 x^6+12 x^4+12 x^2+43$
• $y^2=56 x^6+15 x^5+64 x^4+21 x^3+69 x^2+30 x+66$
• $y^2=7 x^6+32 x^5+69 x^4+69 x^3+42 x^2+41 x+32$
• $y^2=59 x^6+59 x^5+63 x^4+68 x^3+31 x^2+22 x+13$
• $y^2=39 x^6+70 x^5+31 x^4+57 x^3+58 x^2+35 x+20$
• $y^2=56 x^6+20 x^4+20 x^2+56$
• $y^2=x^6+x^3+27$
• $y^2=50 x^6+50 x^4+50 x^2+50$
• $y^2=2 x^6+16 x^5+14 x^4+35 x^3+14 x^2+16 x+2$
• $y^2=43 x^6+13 x^5+53 x^4+24 x^3+33 x^2+52 x+52$
• $y^2=43 x^6+51 x^5+45 x^4+36 x^3+15 x^2+30 x+7$
• $y^2=31 x^6+7 x^5+24 x^4+30 x^3+24 x^2+7 x+31$
• $y^2=10 x^6+51 x^5+62 x^4+24 x^3+62 x^2+51 x+10$
• $y^2=x^6+25 x^3+3$
• $y^2=9 x^6+66 x^5+7 x^4+8 x^3+58 x^2+41 x+10$
• $y^2=15 x^6+26 x^5+x^4+8 x^3+x^2+26 x+15$
• $y^2=26 x^6+42 x^5+55 x^4+58 x^3+3 x^2+62 x+33$
• $y^2=x^6+37 x^3+64$
• $y^2=20 x^6+60 x^5+4 x^4+44 x^3+55 x^2+47 x+39$
• $y^2=32 x^6+44 x^5+50 x^4+35 x^3+50 x^2+44 x+32$
• $y^2=53 x^6+67 x^5+69 x^4+14 x^3+18 x^2+61 x+34$
• $y^2=58 x^6+48 x^5+49 x^4+28 x^3+49 x^2+48 x+58$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.ao^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-6}) \)$)$

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.a_aby	$2$	(not in LMFDB)
2.73.bc_ne	$2$	(not in LMFDB)
2.73.o_et	$3$	(not in LMFDB)