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

• Label: 2.73.v_jt
• 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:	$1 + 21 x + 253 x^{2} + 1533 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.669972317809$, $\pm0.755842394823$
Angle rank:	$2$ (numerical)
Number field:	4.0.571389.1
Galois group:	$D_{4}$
Jacobians:	$40$
Isomorphism classes:	40

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7137$	$28754973$	$150527273481$	$806924151439029$	$4297566449889752832$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$95$	$5395$	$386939$	$28414579$	$2073042950$	$151333535275$	$11047406311715$	$806460059927299$	$58871586620008127$	$4297625831380946350$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 40 curves (of which all are hyperelliptic):

• $y^2=18 x^6+66 x^5+24 x^4+40 x^3+8 x^2+46 x+42$
• $y^2=3 x^6+29 x^5+3 x^4+50 x^3+70 x^2+18 x+13$
• $y^2=66 x^6+32 x^5+54 x^4+42 x^3+21 x^2+69 x+48$
• $y^2=27 x^6+16 x^5+34 x^4+71 x^3+71 x^2+20 x+25$
• $y^2=43 x^6+53 x^5+22 x^4+72 x^3+71 x^2+43 x+69$
• $y^2=11 x^6+38 x^5+25 x^4+53 x^3+25 x^2+44 x+50$
• $y^2=x^6+67 x^5+41 x^4+33 x^3+56 x^2+22 x+6$
• $y^2=29 x^6+31 x^5+41 x^4+35 x^3+x^2+17 x+30$
• $y^2=67 x^6+59 x^5+40 x^4+44 x^3+16 x^2+17 x+33$
• $y^2=23 x^6+47 x^5+4 x^4+22 x^3+15 x^2+65 x+25$
• $y^2=6 x^6+42 x^5+64 x^4+11 x^3+42 x^2+37 x+27$
• $y^2=42 x^6+29 x^5+5 x^4+10 x^3+6 x^2+27 x+55$
• $y^2=25 x^6+17 x^5+57 x^4+20 x^3+60 x^2+21 x+14$
• $y^2=61 x^6+17 x^5+3 x^4+26 x^3+58 x^2+15 x+63$
• $y^2=69 x^6+31 x^5+48 x^4+58 x^3+38 x^2+46 x+27$
• $y^2=8 x^6+38 x^5+34 x^4+30 x^2+38 x+69$
• $y^2=14 x^6+25 x^5+24 x^4+9 x^3+50 x^2+70 x+25$
• $y^2=44 x^6+41 x^5+40 x^4+30 x^3+53 x^2+64 x+53$
• $y^2=17 x^6+5 x^5+59 x^4+16 x^3+36 x^2+60 x+4$
• $y^2=69 x^6+45 x^5+39 x^4+45 x^3+34 x^2+22 x+62$
• and

• $y^2=69 x^6+56 x^5+63 x^4+31 x^3+26 x^2+28 x+31$
• $y^2=69 x^6+48 x^5+5 x^4+19 x^3+15 x^2+37 x+61$
• $y^2=9 x^6+65 x^5+30 x^4+34 x^3+8 x^2+62 x+9$
• $y^2=24 x^6+24 x^5+66 x^4+32 x^3+61 x^2+6 x+35$
• $y^2=14 x^6+24 x^5+5 x^4+4 x^3+68 x^2+44 x+4$
• $y^2=16 x^6+14 x^5+45 x^4+10 x^3+41 x^2+30 x+17$
• $y^2=40 x^6+21 x^5+24 x^4+44 x^3+37 x^2+62 x+3$
• $y^2=71 x^6+27 x^5+3 x^4+22 x^3+34 x^2+29 x+25$
• $y^2=3 x^6+12 x^5+21 x^4+63 x^3+31 x^2+22 x+69$
• $y^2=55 x^6+15 x^5+26 x^4+27 x^3+13 x^2+59 x+20$
• $y^2=48 x^6+52 x^5+31 x^4+14 x^3+69 x^2+70 x+25$
• $y^2=69 x^6+72 x^4+10 x^3+69 x^2+30 x+72$
• $y^2=72 x^6+42 x^5+34 x^4+51 x^3+4 x^2+65 x+6$
• $y^2=3 x^6+14 x^5+50 x^4+11 x^3+57 x^2+13 x$
• $y^2=21 x^6+8 x^5+33 x^4+36 x^3+43 x^2+22 x+16$
• $y^2=4 x^6+23 x^5+50 x^4+23 x^3+59 x^2+11 x+12$
• $y^2=69 x^6+24 x^5+55 x^4+37 x^3+35 x^2+5 x+30$
• $y^2=62 x^6+63 x^5+53 x^4+2 x^3+19 x^2+20 x+6$
• $y^2=31 x^6+64 x^5+34 x^4+10 x^3+42 x^2+4 x+18$
• $y^2=60 x^6+64 x^5+14 x^4+57 x^3+18 x^2+71 x+4$

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 4.0.571389.1.

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.av_jt	$2$	(not in LMFDB)