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

• Label: 2.73.w_kh
• 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:	$( 1 + 11 x + 73 x^{2} )^{2}$
	$1 + 22 x + 267 x^{2} + 1606 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.722612475433$, $\pm0.722612475433$
Angle rank:	$1$ (numerical)
Jacobians:	$47$
Cyclic group of points:	no
Non-cyclic primes:	$5, 17$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7225$	$28676025$	$150497443600$	$807030088475625$	$4297494530644005625$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$96$	$5380$	$386862$	$28418308$	$2073008256$	$151333458190$	$11047411591872$	$806460004164868$	$58871586718976766$	$4297625835989992900$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 47 curves (of which all are hyperelliptic):

• $y^2=32 x^6+x^5+40 x^4+32 x^3+34 x^2+2 x+69$
• $y^2=x^6+10 x^5+70 x^4+23 x^3+65 x^2+63 x+46$
• $y^2=62 x^6+17 x^5+19 x^4+8 x^3+x^2+14 x+28$
• $y^2=41 x^6+59 x^5+32 x^4+55 x^3+71 x^2+45 x+4$
• $y^2=16 x^6+32 x^5+45 x^4+18 x^3+45 x^2+32 x+16$
• $y^2=55 x^6+8 x^5+72 x^4+42 x^3+33 x^2+69 x+10$
• $y^2=5 x^6+5 x^3+11$
• $y^2=48 x^6+20 x^5+28 x^4+70 x^3+14 x^2+5 x+6$
• $y^2=3 x^6+9 x^5+11 x^4+23 x^3+34 x^2+16 x+1$
• $y^2=6 x^6+52 x^5+72 x^4+45 x^3+65 x^2+33 x+32$
• $y^2=47 x^6+64 x^5+60 x^4+58 x^3+38 x^2+34 x+18$
• $y^2=57 x^6+22 x^5+26 x^4+2 x^3+52 x^2+15 x+18$
• $y^2=18 x^6+38 x^5+63 x^4+9 x^3+59 x^2+19 x+71$
• $y^2=17 x^6+70 x^5+56 x^4+23 x^3+62 x^2+48 x+43$
• $y^2=25 x^6+3 x^5+23 x^4+18 x^3+55 x^2+54 x+16$
• $y^2=3 x^6+9 x^5+60 x^4+9 x^3+53 x^2+x+8$
• $y^2=44 x^6+57 x^5+23 x^4+72 x^3+65 x^2+8 x+14$
• $y^2=61 x^6+27 x^5+39 x^4+47 x^3+44 x^2+24 x+41$
• $y^2=51 x^6+63 x^5+4 x^4+41 x^3+55 x^2+1$
• $y^2=36 x^6+13 x^5+38 x^4+48 x^3+71 x^2+15 x+12$
• and

• $y^2=56 x^6+13 x^5+29 x^4+17 x^3+4 x^2+8 x+23$
• $y^2=13 x^6+28 x^5+11 x^4+39 x^3+15 x^2+40 x+13$
• $y^2=72 x^6+63 x^5+37 x^4+25 x^3+38 x^2+56 x+46$
• $y^2=72 x^6+18 x^5+20 x^4+30 x^3+9 x^2+26 x+69$
• $y^2=5 x^6+5 x^3+28$
• $y^2=35 x^6+72 x^5+36 x^4+6 x^3+51 x^2+56 x+40$
• $y^2=62 x^6+47 x^5+4 x^4+24 x^3+19 x^2+43 x+45$
• $y^2=49 x^6+29 x^5+7 x^4+5 x^3+43 x^2+44 x+64$
• $y^2=55 x^6+69 x^5+68 x^4+35 x^3+27 x^2+3 x+61$
• $y^2=14 x^6+28 x^5+57 x^4+41 x^3+46 x^2+17 x+44$
• $y^2=55 x^6+55 x^5+11 x^4+18 x^3+42 x^2+32 x+16$
• $y^2=44 x^6+22 x^5+69 x^4+46 x^3+16 x^2+60 x+31$
• $y^2=5 x^6+43 x^3+15$
• $y^2=55 x^6+59 x^5+28 x^4+41 x^3+55 x^2+38 x+8$
• $y^2=71 x^6+57 x^5+50 x^4+30 x^3+69 x^2+2 x+54$
• $y^2=22 x^6+11 x^5+43 x^4+42 x^3+40 x^2+27 x+32$
• $y^2=11 x^6+21 x^5+28 x^4+46 x^3+63 x^2+47 x+58$
• $y^2=51 x^6+52 x^5+x^4+70 x^3+35 x^2+44 x+56$
• $y^2=45 x^6+57 x^5+42 x^4+30 x^3+45 x^2+66 x+20$
• $y^2=34 x^6+26 x^5+18 x^4+42 x^3+49 x^2+30 x+60$
• $y^2=62 x^6+15 x^5+21 x^4+18 x^3+60 x^2+42 x+58$
• $y^2=37 x^6+28 x^4+65 x^3+53 x^2+41$
• $y^2=11 x^6+49 x^5+56 x^4+12 x^3+43 x^2+46 x+68$
• $y^2=18 x^6+40 x^5+51 x^4+45 x^3+68 x^2+63 x+67$
• $y^2=5 x^6+22 x^3+58$
• $y^2=69 x^6+33 x^5+56 x^4+7 x^3+50 x^2+11 x+58$
• $y^2=14 x^6+50 x^5+41 x^4+62 x^3+41 x^2+50 x+14$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.l^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-19}) \)$)$

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.aw_kh	$2$	(not in LMFDB)
2.73.a_z	$2$	(not in LMFDB)
2.73.al_bw	$3$	(not in LMFDB)