Abelian variety isogeny class 2.71.ad_ey over $\F_{71}$

• Label: 2.71.ad_ey
• Base field: $\F_{71}$
• 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:	$\F_{71}$
Dimension:	$2$
L-polynomial:	$1 - 3 x + 128 x^{2} - 213 x^{3} + 5041 x^{4}$
Frobenius angles:	$\pm0.393553922135$, $\pm0.547990108335$
Angle rank:	$2$ (numerical)
Number field:	4.0.297203400.1
Galois group:	$D_{4}$
Jacobians:	$48$
Isomorphism classes:	96
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4954$	$26682244$	$128274417400$	$645483398997024$	$3255195966763436734$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$69$	$5289$	$358398$	$25401049$	$1804202979$	$128100424218$	$9095119240269$	$645753558517009$	$45848501080611858$	$3255243547702857729$

Jacobians and polarizations

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

• $y^2=43 x^6+8 x^5+9 x^4+27 x^3+52 x^2+x+70$
• $y^2=59 x^6+46 x^5+57 x^4+9 x^3+34 x^2+50 x+55$
• $y^2=23 x^6+8 x^5+15 x^4+22 x^3+29 x^2+17 x+23$
• $y^2=42 x^6+x^5+10 x^4+34 x^3+37 x^2+38 x+38$
• $y^2=23 x^6+42 x^5+20 x^4+42 x^3+39 x^2+19 x+69$
• $y^2=25 x^6+37 x^5+x^4+24 x^2+11 x+4$
• $y^2=37 x^6+28 x^5+43 x^4+26 x^3+66 x^2+68 x+38$
• $y^2=22 x^6+24 x^5+33 x^4+40 x^3+63 x^2+57 x+67$
• $y^2=8 x^6+5 x^5+33 x^4+69 x^3+5 x^2+5 x+48$
• $y^2=21 x^6+14 x^5+38 x^4+35 x^3+68 x^2+30 x+14$
• $y^2=11 x^6+58 x^5+8 x^4+57 x^3+8 x^2+69 x+69$
• $y^2=18 x^6+47 x^5+26 x^4+10 x^3+54 x^2+65 x+2$
• $y^2=28 x^6+26 x^5+38 x^4+24 x^3+12 x^2+42 x+66$
• $y^2=49 x^6+54 x^5+52 x^4+54 x^3+25 x^2+16 x+22$
• $y^2=30 x^6+18 x^4+18 x^3+25 x^2+34 x+32$
• $y^2=13 x^6+47 x^5+54 x^4+69 x^3+53 x^2+63 x+27$
• $y^2=9 x^6+53 x^5+45 x^4+27 x^3+25 x^2+40 x+35$
• $y^2=36 x^6+53 x^5+66 x^4+30 x^3+42 x^2+16 x+35$
• $y^2=27 x^6+34 x^5+20 x^4+14 x^3+6 x^2+39 x+20$
• $y^2=13 x^6+23 x^5+15 x^4+52 x^3+66 x^2+49 x+8$
• and

• $y^2=65 x^6+68 x^5+43 x^4+18 x^3+45 x^2+65 x+51$
• $y^2=21 x^6+14 x^5+46 x^4+61 x^3+24 x^2+58 x+44$
• $y^2=4 x^6+3 x^5+41 x^4+61 x^3+50 x^2+67 x+9$
• $y^2=23 x^6+57 x^5+26 x^4+39 x^3+56 x^2+14 x+16$
• $y^2=49 x^6+2 x^5+4 x^4+46 x^3+x^2+12 x+51$
• $y^2=9 x^6+59 x^5+25 x^4+67 x^3+70 x^2+36 x+60$
• $y^2=62 x^6+14 x^5+36 x^4+43 x^3+57 x^2+26 x+50$
• $y^2=69 x^6+10 x^5+53 x^4+54 x^3+14 x^2+26 x+36$
• $y^2=x^6+29 x^5+3 x^4+14 x^3+47 x^2+59 x+67$
• $y^2=45 x^6+x^5+60 x^4+46 x^3+33 x^2+62 x+30$
• $y^2=41 x^6+5 x^5+55 x^4+61 x^3+2 x^2+38 x+67$
• $y^2=49 x^6+19 x^5+25 x^4+9 x^3+11 x^2+17 x+22$
• $y^2=38 x^6+58 x^5+55 x^4+54 x^3+45 x^2+17 x+8$
• $y^2=67 x^6+58 x^5+41 x^4+20 x^3+65 x^2+66 x+69$
• $y^2=39 x^6+30 x^5+65 x^4+68 x^3+55 x^2+30 x+53$
• $y^2=25 x^6+3 x^5+44 x^4+16 x^3+29 x^2+49 x+12$
• $y^2=59 x^6+46 x^5+69 x^4+68 x^3+30 x^2+70 x+60$
• $y^2=10 x^6+23 x^5+60 x^4+67 x^3+55 x^2+51 x+42$
• $y^2=50 x^6+22 x^5+59 x^4+16 x^3+67 x^2+15 x+35$
• $y^2=70 x^6+4 x^5+62 x^4+16 x^3+41 x^2+51 x+14$
• $y^2=5 x^6+12 x^5+15 x^4+6 x^3+9 x^2+57 x+19$
• $y^2=14 x^6+11 x^5+19 x^4+37 x^3+3 x^2+36 x+68$
• $y^2=17 x^6+12 x^5+43 x^4+33 x^3+65 x^2+45 x+64$
• $y^2=x^6+64 x^5+42 x^4+60 x^3+13 x^2+24 x+29$
• $y^2=6 x^6+x^5+40 x^4+70 x^3+33 x^2+21 x+15$
• $y^2=47 x^6+34 x^5+64 x^4+42 x^3+36 x^2+64 x+67$
• $y^2=20 x^6+42 x^5+66 x^4+70 x^3+53 x^2+7 x+30$
• $y^2=54 x^6+5 x^5+x^4+64 x^3+59 x^2+7 x+7$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{71}$.

Endomorphism algebra over $\F_{71}$

The endomorphism algebra of this simple isogeny class is 4.0.297203400.1.

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
2.71.d_ey	$2$	(not in LMFDB)