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

• Label: 2.79.z_lr
• 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:	$1 + 25 x + 303 x^{2} + 1975 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.672021317160$, $\pm0.850601564004$
Angle rank:	$2$ (numerical)
Number field:	4.0.375525.3
Galois group:	$D_{4}$
Jacobians:	$48$
Isomorphism classes:	60
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8545$	$38837025$	$242508800455$	$1517526497832525$	$9468182234892898000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$105$	$6223$	$491865$	$38960803$	$3077025900$	$243087408763$	$19203905555835$	$1517108903160403$	$119851594973360295$	$9468276086669098798$

Jacobians and polarizations

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

• $y^2=45 x^6+65 x^5+70 x^4+43 x^3+60 x^2+64 x+13$
• $y^2=13 x^6+62 x^5+10 x^4+3 x^3+71 x^2+6 x+57$
• $y^2=18 x^6+13 x^5+78 x^4+70 x^3+32 x^2+77 x+65$
• $y^2=17 x^6+44 x^5+5 x^4+5 x^3+49 x^2+16 x+46$
• $y^2=16 x^6+50 x^5+49 x^4+11 x^3+48 x^2+2 x+22$
• $y^2=34 x^6+x^5+31 x^4+46 x^3+63 x^2+73 x+15$
• $y^2=12 x^6+53 x^5+72 x^4+15 x^3+67 x^2+4 x+51$
• $y^2=38 x^6+35 x^5+29 x^4+50 x^3+34 x^2+14 x+48$
• $y^2=25 x^6+57 x^5+23 x^4+51 x^3+35 x^2+22$
• $y^2=14 x^6+65 x^5+54 x^4+9 x^3+62 x^2+11 x+10$
• $y^2=35 x^6+26 x^5+6 x^4+18 x^3+39 x^2+23 x+63$
• $y^2=25 x^6+56 x^5+x^4+37 x^3+51 x^2+77 x+24$
• $y^2=27 x^6+15 x^5+8 x^4+31 x^3+13 x^2+27 x+7$
• $y^2=32 x^6+37 x^5+69 x^4+34 x^3+46 x^2+69 x+39$
• $y^2=66 x^6+30 x^5+2 x^4+68 x^3+14 x^2+x+76$
• $y^2=47 x^6+71 x^5+28 x^4+70 x^3+x^2+71 x+61$
• $y^2=4 x^6+36 x^5+51 x^4+27 x^3+45 x^2+18 x+61$
• $y^2=55 x^6+59 x^5+50 x^4+68 x^3+48 x^2+26 x+11$
• $y^2=76 x^6+63 x^5+38 x^4+71 x^3+23 x^2+50 x+8$
• $y^2=47 x^6+32 x^5+78 x^4+38 x^3+65 x^2+x+1$
• and

• $y^2=x^6+53 x^5+55 x^4+63 x^3+x^2+66 x+54$
• $y^2=21 x^6+75 x^5+5 x^4+22 x^3+43 x^2+12 x+14$
• $y^2=32 x^6+57 x^5+38 x^4+20 x^3+78 x^2+3 x+20$
• $y^2=63 x^6+33 x^5+48 x^4+9 x^3+56 x^2+75 x+8$
• $y^2=25 x^6+61 x^5+60 x^4+52 x^3+37 x^2+36 x+45$
• $y^2=38 x^6+26 x^5+38 x^4+14 x^3+3 x^2+45 x+19$
• $y^2=10 x^6+11 x^5+3 x^4+37 x^3+30 x^2+46 x+44$
• $y^2=44 x^6+52 x^5+8 x^4+69 x^3+10 x^2+34 x+36$
• $y^2=31 x^6+45 x^5+21 x^4+69 x^3+35 x^2+42 x+22$
• $y^2=10 x^6+47 x^5+34 x^4+60 x^3+51 x^2+8 x+47$
• $y^2=78 x^6+42 x^5+7 x^4+44 x^3+54 x^2+54 x+5$
• $y^2=45 x^6+47 x^5+45 x^4+29 x^3+14 x^2+21 x+25$
• $y^2=6 x^6+25 x^5+4 x^4+54 x^3+4 x^2+62 x+71$
• $y^2=34 x^6+7 x^5+14 x^4+30 x^3+32 x^2+60 x+41$
• $y^2=20 x^6+16 x^5+40 x^4+14 x^3+38 x^2+20 x+62$
• $y^2=13 x^6+75 x^5+11 x^4+20 x^3+36 x^2+39 x+56$
• $y^2=52 x^6+32 x^5+66 x^4+54 x^3+63 x^2+58 x+73$
• $y^2=10 x^5+2 x^4+2 x^3+22 x^2+2 x+50$
• $y^2=44 x^6+28 x^5+60 x^4+36 x^3+64 x^2+37 x+21$
• $y^2=x^6+9 x^5+34 x^4+40 x^3+19 x^2+16 x+5$
• $y^2=12 x^6+74 x^5+18 x^4+5 x^3+77 x^2+44 x+71$
• $y^2=20 x^6+47 x^5+63 x^4+49 x^3+21 x^2+8$
• $y^2=54 x^6+58 x^5+75 x^4+66 x^3+57 x^2+26 x+52$
• $y^2=22 x^6+12 x^5+63 x^4+32 x^3+44 x^2+45 x+44$
• $y^2=68 x^6+55 x^5+27 x^4+28 x^3+76 x^2+9 x+11$
• $y^2=20 x^6+15 x^5+3 x^4+3 x^3+32 x^2+27 x+13$
• $y^2=19 x^6+31 x^5+39 x^4+64 x^3+24 x^2+31 x+21$
• $y^2=67 x^6+10 x^5+37 x^3+65 x^2+8 x+73$

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 4.0.375525.3.

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.az_lr	$2$	(not in LMFDB)