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

• Label: 2.73.aw_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:	$\pm0.277387524567$, $\pm0.277387524567$
Angle rank:	$1$ (numerical)
Jacobians:	$47$
Cyclic group of points:	no
Non-cyclic primes:	$3, 7$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3969$	$28676025$	$152174889216$	$807030088475625$	$4297757139061247169$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$52$	$5380$	$391174$	$28418308$	$2073134932$	$151333458190$	$11047385446324$	$806460004164868$	$58871586697559062$	$4297625835989992900$

Jacobians and polarizations

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

• $y^2=21 x^6+44 x^5+8 x^4+21 x^3+36 x^2+15 x+43$
• $y^2=5 x^6+50 x^5+58 x^4+42 x^3+33 x^2+23 x+11$
• $y^2=18 x^6+12 x^5+22 x^4+40 x^3+5 x^2+70 x+67$
• $y^2=59 x^6+3 x^5+14 x^4+56 x^3+63 x^2+6 x+20$
• $y^2=47 x^6+21 x^5+9 x^4+62 x^3+9 x^2+21 x+47$
• $y^2=11 x^6+60 x^5+29 x^4+23 x^3+65 x^2+43 x+2$
• $y^2=x^6+x^3+46$
• $y^2=21 x^6+27 x^5+67 x^4+58 x^3+70 x^2+25 x+30$
• $y^2=59 x^6+31 x^5+46 x^4+63 x^3+36 x^2+47 x+44$
• $y^2=45 x^6+25 x^5+29 x^4+9 x^3+13 x^2+65 x+21$
• $y^2=24 x^6+42 x^5+12 x^4+70 x^3+66 x^2+36 x+62$
• $y^2=66 x^6+37 x^5+57 x^4+10 x^3+41 x^2+2 x+17$
• $y^2=17 x^6+44 x^5+23 x^4+45 x^3+3 x^2+22 x+63$
• $y^2=12 x^6+58 x^5+61 x^4+42 x^3+18 x^2+21 x+69$
• $y^2=5 x^6+59 x^5+63 x^4+62 x^3+11 x^2+40 x+47$
• $y^2=15 x^6+45 x^5+8 x^4+45 x^3+46 x^2+5 x+40$
• $y^2=x^6+66 x^5+42 x^4+68 x^3+33 x^2+40 x+70$
• $y^2=13 x^6+62 x^5+49 x^4+16 x^3+x^2+47 x+59$
• $y^2=36 x^6+23 x^5+20 x^4+59 x^3+56 x^2+5$
• $y^2=34 x^6+65 x^5+44 x^4+21 x^3+63 x^2+2 x+60$
• and

• $y^2=61 x^6+65 x^5+72 x^4+12 x^3+20 x^2+40 x+42$
• $y^2=65 x^6+67 x^5+55 x^4+49 x^3+2 x^2+54 x+65$
• $y^2=29 x^6+71 x^5+22 x^4+5 x^3+66 x^2+55 x+53$
• $y^2=68 x^6+17 x^5+27 x^4+4 x^3+45 x^2+57 x+53$
• $y^2=x^6+x^3+64$
• $y^2=29 x^6+68 x^5+34 x^4+30 x^3+36 x^2+61 x+54$
• $y^2=27 x^6+24 x^5+30 x^4+34 x^3+33 x^2+67 x+9$
• $y^2=26 x^6+72 x^5+35 x^4+25 x^3+69 x^2+x+28$
• $y^2=56 x^6+53 x^5+48 x^4+29 x^3+62 x^2+15 x+13$
• $y^2=32 x^6+64 x^5+26 x^4+52 x^3+53 x^2+18 x+38$
• $y^2=56 x^6+56 x^5+55 x^4+17 x^3+64 x^2+14 x+7$
• $y^2=x^6+37 x^5+53 x^4+11 x^3+7 x^2+8 x+9$
• $y^2=x^6+67 x^3+3$
• $y^2=11 x^6+41 x^5+64 x^4+52 x^3+11 x^2+66 x+60$
• $y^2=63 x^6+66 x^5+31 x^4+4 x^3+53 x^2+10 x+51$
• $y^2=37 x^6+55 x^5+69 x^4+64 x^3+54 x^2+62 x+14$
• $y^2=55 x^6+32 x^5+67 x^4+11 x^3+23 x^2+16 x+71$
• $y^2=36 x^6+41 x^5+5 x^4+58 x^3+29 x^2+x+61$
• $y^2=6 x^6+66 x^5+64 x^4+4 x^3+6 x^2+38 x+27$
• $y^2=36 x^6+49 x^5+62 x^4+23 x^3+39 x^2+6 x+12$
• $y^2=27 x^6+3 x^5+48 x^4+62 x^3+12 x^2+23 x+70$
• $y^2=39 x^6+67 x^4+33 x^3+46 x^2+59$
• $y^2=46 x^6+39 x^5+55 x^4+17 x^3+67 x^2+53 x+72$
• $y^2=17 x^6+54 x^5+36 x^4+6 x^3+48 x^2+23 x+43$
• $y^2=x^6+19 x^3+70$
• $y^2=43 x^6+65 x^5+55 x^4+16 x^3+10 x^2+46 x+70$
• $y^2=32 x^6+10 x^5+52 x^4+27 x^3+52 x^2+10 x+32$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.al^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.a_z	$2$	(not in LMFDB)
2.73.w_kh	$2$	(not in LMFDB)
2.73.l_bw	$3$	(not in LMFDB)