Abelian variety isogeny class 2.79.l_hb over $\F_{79}$

• Label: 2.79.l_hb
• Base field: $\F_{79}$
• 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:	$\F_{79}$
Dimension:	$2$
L-polynomial:	$1 + 11 x + 183 x^{2} + 869 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.557772928488$, $\pm0.644417188647$
Angle rank:	$2$ (numerical)
Number field:	4.0.34417845.1
Galois group:	$D_{4}$
Jacobians:	$48$
Isomorphism classes:	48
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7305$	$40506225$	$242053563735$	$1516862734090125$	$9468806691510452400$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$6487$	$490939$	$38943763$	$3077228836$	$243087011827$	$19203900914569$	$1517108869480243$	$119851596113806861$	$9468276080065102702$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 48 curves (of which all are hyperelliptic):

• $y^2=20 x^6+72 x^5+53 x^4+75 x^3+35 x^2+57 x+72$
• $y^2=78 x^6+73 x^5+41 x^4+8 x^3+25 x^2+76 x+22$
• $y^2=36 x^6+69 x^5+37 x^4+62 x^3+44 x^2+31 x+33$
• $y^2=69 x^6+15 x^5+55 x^4+14 x^3+10 x^2+31 x+22$
• $y^2=77 x^6+24 x^5+44 x^4+2 x^3+16 x^2+x+33$
• $y^2=34 x^6+71 x^5+58 x^4+9 x^3+45 x^2+53 x+50$
• $y^2=9 x^6+54 x^5+19 x^4+14 x^3+77 x^2+53 x+62$
• $y^2=55 x^6+12 x^5+14 x^4+34 x^3+33 x^2+63 x+46$
• $y^2=20 x^6+62 x^5+53 x^4+72 x^3+13 x^2+36 x+62$
• $y^2=49 x^6+51 x^5+65 x^4+76 x^3+44 x^2+73 x+53$
• $y^2=48 x^6+12 x^5+64 x^4+75 x^3+65 x^2+57 x+47$
• $y^2=4 x^6+62 x^5+10 x^4+42 x^3+74 x^2+3 x+37$
• $y^2=6 x^6+54 x^5+73 x^4+29 x^3+30 x^2+53 x+74$
• $y^2=42 x^6+11 x^5+9 x^4+38 x^3+6 x^2+4 x+77$
• $y^2=3 x^6+31 x^5+35 x^4+2 x^3+38 x^2+53 x+62$
• $y^2=21 x^6+58 x^5+10 x^4+5 x^3+3 x^2+75 x+2$
• $y^2=67 x^6+21 x^5+33 x^4+2 x^3+12 x^2+71 x+38$
• $y^2=62 x^6+31 x^5+5 x^4+70 x^3+2 x^2+75 x+40$
• $y^2=46 x^6+63 x^5+49 x^4+10 x^3+18 x^2+66 x+16$
• $y^2=26 x^6+75 x^5+10 x^4+37 x^3+74 x^2+42 x+68$
• and

• $y^2=23 x^6+21 x^5+60 x^4+76 x^3+70 x^2+20 x+24$
• $y^2=64 x^6+37 x^5+12 x^4+61 x^3+8 x^2+13 x+4$
• $y^2=74 x^6+64 x^5+24 x^4+46 x^3+51 x^2+33 x+67$
• $y^2=42 x^6+53 x^5+54 x^3+63 x^2+29 x+41$
• $y^2=70 x^6+46 x^5+21 x^4+9 x^3+51 x^2+7 x+64$
• $y^2=67 x^6+59 x^5+x^4+49 x^3+28 x^2+11 x+24$
• $y^2=16 x^6+53 x^5+78 x^4+16 x^3+57 x^2+13 x+31$
• $y^2=11 x^6+49 x^5+16 x^4+13 x^3+63 x^2+46 x+18$
• $y^2=48 x^5+x^4+71 x^3+75 x^2+15 x+24$
• $y^2=13 x^6+36 x^5+26 x^4+51 x^3+10 x^2+40 x+25$
• $y^2=2 x^6+6 x^5+23 x^3+77 x^2+51 x+74$
• $y^2=22 x^6+45 x^5+50 x^4+46 x^3+45 x^2+71 x+73$
• $y^2=52 x^6+14 x^5+53 x^4+65 x^3+27 x^2+42 x+33$
• $y^2=53 x^6+64 x^5+32 x^4+61 x^3+36 x^2+7 x+12$
• $y^2=20 x^6+56 x^5+2 x^4+78 x^3+6 x^2+10 x+54$
• $y^2=63 x^6+17 x^5+23 x^4+64 x^3+64 x^2+35 x+8$
• $y^2=28 x^6+78 x^5+18 x^4+69 x^3+12 x^2+71 x+1$
• $y^2=54 x^6+41 x^5+11 x^4+37 x^3+54 x^2+65 x+42$
• $y^2=60 x^6+26 x^5+54 x^4+72 x^3+71 x^2+44 x+74$
• $y^2=67 x^6+2 x^5+33 x^4+67 x^3+74 x^2+28 x+11$
• $y^2=x^6+28 x^5+27 x^4+2 x^3+6 x^2+41 x+57$
• $y^2=32 x^6+57 x^5+34 x^4+68 x^3+65 x^2+76 x+47$
• $y^2=74 x^6+32 x^5+18 x^4+14 x^3+75 x^2+73 x+18$
• $y^2=32 x^6+43 x^5+23 x^4+18 x^3+54 x^2+63 x+42$
• $y^2=73 x^6+28 x^5+59 x^4+53 x^3+29 x^2+62 x+1$
• $y^2=78 x^6+16 x^5+26 x^4+24 x^3+55 x^2+17 x+33$
• $y^2=8 x^6+62 x^5+74 x^4+55 x^3+5 x^2+76 x+67$
• $y^2=6 x^6+55 x^5+78 x^4+58 x^3+73 x^2+70 x+52$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{79}$.

Endomorphism algebra over $\F_{79}$

The endomorphism algebra of this simple isogeny class is 4.0.34417845.1.

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
2.79.al_hb	$2$	(not in LMFDB)