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

• Label: 2.79.ag_gl
• Base field: $\F_{79}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{79}$
Dimension:	$2$
L-polynomial:	$( 1 - 3 x + 79 x^{2} )^{2}$
	$1 - 6 x + 167 x^{2} - 474 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.446022689903$, $\pm0.446022689903$
Angle rank:	$1$ (numerical)
Jacobians:	$42$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$5929$	$40844881$	$243763388176$	$1516351870571769$	$9467764116595864849$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$6540$	$494408$	$38930644$	$3076890014$	$243088491966$	$19203925239986$	$1517108776788964$	$119851594599213272$	$9468276081092922300$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 42 curves (of which all are hyperelliptic):

• $y^2=43 x^6+64 x^5+70 x^4+22 x^3+8 x^2+58 x+14$
• $y^2=4 x^6+56 x^5+41 x^3+56 x+4$
• $y^2=73 x^6+63 x^5+76 x^4+60 x^3+76 x^2+63 x+73$
• $y^2=53 x^6+24 x^5+17 x^4+59 x^3+17 x^2+24 x+53$
• $y^2=78 x^6+39 x^5+14 x^4+47 x^3+57 x^2+68 x+43$
• $y^2=5 x^6+11 x^5+27 x^4+60 x^3+27 x^2+11 x+5$
• $y^2=38 x^6+50 x^5+65 x^4+52 x^3+12 x^2+34 x+57$
• $y^2=37 x^6+71 x^5+71 x^4+61 x^3+71 x^2+71 x+37$
• $y^2=57 x^6+18 x^5+74 x^4+78 x^3+51 x^2+61 x+68$
• $y^2=58 x^6+18 x^5+8 x^4+41 x^3+66 x^2+48 x+59$
• $y^2=55 x^6+64 x^5+41 x^4+61 x^3+23 x^2+66 x+54$
• $y^2=65 x^6+41 x^5+43 x^4+35 x^3+49 x^2+66 x+9$
• $y^2=61 x^6+52 x^5+39 x^4+56 x^3+73 x^2+63 x+46$
• $y^2=x^6+70 x^5+43 x^4+3 x^3+15 x^2+21 x+36$
• $y^2=23 x^6+38 x^5+21 x^4+65 x^3+60 x^2+75 x+8$
• $y^2=54 x^6+52 x^5+42 x^4+41 x^3+41 x^2+64 x+32$
• $y^2=12 x^6+20 x^5+3 x^4+34 x^3+9 x^2+51 x+23$
• $y^2=15 x^6+65 x^5+24 x^4+2 x^3+30 x^2+77 x+32$
• $y^2=37 x^6+36 x^5+33 x^4+11 x^3+33 x^2+36 x+37$
• $y^2=48 x^6+59 x^5+73 x^4+18 x^3+73 x^2+59 x+48$
• and

• $y^2=20 x^6+59 x^5+56 x^4+56 x^3+56 x^2+59 x+20$
• $y^2=35 x^6+6 x^5+24 x^4+40 x^3+77 x^2+65 x+9$
• $y^2=35 x^6+28 x^5+44 x^4+11 x^3+44 x^2+28 x+35$
• $y^2=43 x^6+41 x^5+9 x^4+20 x^3+34 x^2+48 x+20$
• $y^2=2 x^6+62 x^5+47 x^4+35 x^3+15 x^2+69 x+4$
• $y^2=62 x^6+43 x^5+22 x^4+53 x^3+60 x^2+61 x+72$
• $y^2=56 x^6+45 x^5+70 x^4+24 x^3+24 x^2+54 x+30$
• $y^2=61 x^6+x^5+17 x^4+14 x^3+14 x^2+61 x+6$
• $y^2=55 x^6+x^5+26 x^4+43 x^3+39 x^2+11 x+72$
• $y^2=14 x^6+8 x^5+44 x^4+36 x^3+x^2+60 x+15$
• $y^2=x^6+38 x^5+34 x^4+52 x^3+14 x^2+13 x+44$
• $y^2=72 x^6+66 x^5+71 x^4+13 x^3+75 x^2+73 x+72$
• $y^2=23 x^6+52 x^5+39 x^4+51 x^3+41 x^2+57 x+63$
• $y^2=75 x^6+46 x^5+75 x^4+37 x^3+75 x^2+46 x+75$
• $y^2=14 x^6+59 x^5+69 x^4+63 x^3+31 x^2+37 x+20$
• $y^2=11 x^6+5 x^5+55 x^4+47 x^3+30 x^2+25 x+74$
• $y^2=66 x^6+40 x^5+2 x^4+28 x^3+46 x^2+22 x+61$
• $y^2=38 x^6+47 x^5+52 x^4+77 x^3+60 x^2+46 x+43$
• $y^2=34 x^6+10 x^5+27 x^4+52 x^3+26 x^2+41 x+23$
• $y^2=59 x^6+76 x^5+63 x^4+69 x^3+12 x^2+13 x+61$
• $y^2=77 x^6+62 x^5+38 x^4+38 x^2+62 x+77$
• $y^2=22 x^6+61 x^5+13 x^4+28 x^3+13 x^2+61 x+22$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.ad^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-307}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.79.a_ft	$2$	(not in LMFDB)
2.79.g_gl	$2$	(not in LMFDB)
2.79.d_acs	$3$	(not in LMFDB)