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

• Label: 2.79.d_gd
• 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:	$1 + 3 x + 159 x^{2} + 237 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.506840135899$, $\pm0.547050527077$
Angle rank:	$2$ (numerical)
Number field:	4.0.2441125.2
Galois group:	$D_{4}$
Jacobians:	$32$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6641$	$40915201$	$242746819391$	$1516220993761645$	$9468542648911869296$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$83$	$6551$	$492347$	$38927283$	$3077143028$	$243089056451$	$19203900137897$	$1517108703661363$	$119851596788162213$	$9468276089208842606$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 32 curves (of which all are hyperelliptic):

• $y^2=61 x^6+4 x^5+63 x^4+48 x^3+74 x^2+20 x+24$
• $y^2=12 x^6+71 x^5+52 x^4+31 x^3+32 x^2+30 x+30$
• $y^2=15 x^6+39 x^5+65 x^4+57 x^3+57 x^2+40 x+24$
• $y^2=4 x^6+26 x^5+60 x^4+70 x^3+77 x^2+64 x+50$
• $y^2=72 x^6+30 x^5+37 x^3+13 x^2+78 x+75$
• $y^2=25 x^6+39 x^5+62 x^4+12 x^3+6 x^2+45 x+13$
• $y^2=17 x^5+14 x^4+74 x^3+74 x^2+15 x+12$
• $y^2=30 x^6+23 x^5+67 x^4+x^3+24 x^2+57 x+78$
• $y^2=10 x^6+56 x^5+64 x^4+5 x^3+76 x^2+11 x+69$
• $y^2=77 x^6+24 x^5+12 x^4+44 x^3+24 x^2+52 x+20$
• $y^2=35 x^6+6 x^5+65 x^3+73 x^2+28 x+39$
• $y^2=5 x^6+63 x^5+15 x^4+74 x^3+55 x^2+32 x+59$
• $y^2=65 x^6+68 x^5+6 x^4+8 x^3+30 x^2+50 x+40$
• $y^2=59 x^6+12 x^5+23 x^4+24 x^3+71 x^2+56 x+12$
• $y^2=50 x^6+52 x^5+17 x^4+66 x^3+32 x^2+10 x+75$
• $y^2=3 x^6+15 x^5+16 x^4+10 x^3+71 x^2+67 x$
• $y^2=32 x^6+15 x^5+44 x^4+61 x^3+47 x^2+57 x+8$
• $y^2=16 x^6+70 x^5+56 x^4+59 x^3+16 x^2+48 x+71$
• $y^2=32 x^6+43 x^5+28 x^4+17 x^3+25 x^2+39 x+20$
• $y^2=39 x^6+39 x^5+73 x^4+74 x^3+70 x^2+66 x+61$
• and

• $y^2=49 x^6+32 x^5+49 x^4+54 x^3+54 x^2+65 x+65$
• $y^2=8 x^6+76 x^5+26 x^4+53 x^3+4 x^2+50 x+21$
• $y^2=4 x^6+78 x^5+77 x^4+18 x^3+76 x^2+33 x+60$
• $y^2=29 x^6+71 x^5+40 x^4+42 x^3+19 x^2+71 x+32$
• $y^2=38 x^6+25 x^5+62 x^4+36 x^3+30 x^2+38 x+5$
• $y^2=31 x^6+74 x^5+51 x^4+41 x^3+42 x^2+3 x+22$
• $y^2=28 x^6+16 x^5+18 x^4+64 x^3+49 x^2+9 x+25$
• $y^2=45 x^6+29 x^5+38 x^4+6 x^3+50 x^2+54 x+43$
• $y^2=77 x^6+46 x^5+40 x^4+33 x^3+4 x^2+69 x+58$
• $y^2=32 x^6+44 x^5+54 x^4+77 x^3+14 x^2+76 x+58$
• $y^2=5 x^6+62 x^5+26 x^4+58 x^3+24 x^2+53 x+32$
• $y^2=66 x^6+9 x^5+42 x^4+52 x^3+61 x^2+16 x+64$

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 4.0.2441125.2.

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.ad_gd	$2$	(not in LMFDB)