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

• Label: 2.79.av_je
• 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:	$( 1 - 16 x + 79 x^{2} )( 1 - 5 x + 79 x^{2} )$
	$1 - 21 x + 238 x^{2} - 1659 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.143514932644$, $\pm0.409243695363$
Angle rank:	$2$ (numerical)
Jacobians:	$96$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4800$	$39168000$	$243460857600$	$1517018158080000$	$9468153888102984000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$59$	$6277$	$493796$	$38947753$	$3077016689$	$243088211662$	$19203925734311$	$1517108930311153$	$119851596027327404$	$9468276077975558077$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 96 curves (of which all are hyperelliptic):

• $y^2=70 x^6+38 x^5+76 x^4+57 x^3+47 x^2+41 x+58$
• $y^2=64 x^6+2 x^5+38 x^4+53 x^3+60 x^2+57 x+3$
• $y^2=30 x^6+44 x^5+46 x^4+68 x^3+31 x^2+61 x+34$
• $y^2=67 x^6+47 x^5+6 x^4+56 x^3+66 x^2+40 x+30$
• $y^2=71 x^6+32 x^5+16 x^4+36 x^3+19 x^2+68 x+24$
• $y^2=37 x^6+11 x^5+69 x^4+3 x^3+65 x^2+7 x+15$
• $y^2=55 x^6+63 x^5+7 x^4+60 x^3+64 x^2+11 x+6$
• $y^2=54 x^6+42 x^5+77 x^4+27 x^3+6 x^2+62 x+22$
• $y^2=78 x^6+46 x^5+32 x^4+76 x^3+28 x^2+78 x+46$
• $y^2=15 x^6+63 x^5+69 x^4+44 x^3+49 x^2+18 x+39$
• $y^2=12 x^6+42 x^5+2 x^4+14 x^3+75 x^2+19 x+13$
• $y^2=24 x^6+25 x^5+73 x^4+15 x^3+12 x^2+18 x+1$
• $y^2=4 x^6+25 x^5+46 x^4+20 x^3+38 x^2+63 x+51$
• $y^2=41 x^6+10 x^5+48 x^4+52 x^3+24 x^2+27 x+24$
• $y^2=22 x^6+47 x^5+61 x^4+63 x^3+23 x^2+69 x+50$
• $y^2=25 x^6+8 x^5+15 x^4+29 x^3+28 x^2+3 x+46$
• $y^2=x^6+8 x^5+40 x^4+41 x^3+x^2+28 x+68$
• $y^2=4 x^6+78 x^5+2 x^4+6 x^3+35 x^2+47 x+58$
• $y^2=30 x^6+7 x^5+3 x^4+72 x^3+74 x^2+31 x+15$
• $y^2=22 x^6+24 x^5+28 x^4+53 x^3+49 x^2+45 x+57$
• and

• $y^2=78 x^6+25 x^5+39 x^4+75 x^3+48 x^2+61 x+27$
• $y^2=72 x^6+74 x^5+55 x^4+12 x^3+3 x^2+43 x+59$
• $y^2=20 x^6+44 x^5+59 x^4+42 x^3+x^2+5 x+34$
• $y^2=27 x^6+77 x^5+27 x^4+21 x^3+66 x^2+62 x+8$
• $y^2=61 x^6+33 x^4+67 x^3+35 x^2+26 x+15$
• $y^2=40 x^6+15 x^5+40 x^4+53 x^3+62 x^2+58 x+14$
• $y^2=57 x^6+34 x^5+11 x^4+6 x^3+23 x^2+77 x+55$
• $y^2=51 x^6+x^5+68 x^4+76 x^3+68 x^2+78 x+25$
• $y^2=63 x^6+20 x^5+3 x^4+58 x^3+x^2+5 x+58$
• $y^2=43 x^6+20 x^5+43 x^4+76 x^3+62 x+45$
• $y^2=43 x^6+9 x^5+37 x^4+76 x^3+18 x^2+69 x+1$
• $y^2=22 x^6+42 x^5+3 x^4+10 x^3+60 x^2+65 x+28$
• $y^2=44 x^6+10 x^5+27 x^4+44 x^3+38 x^2+35 x+23$
• $y^2=38 x^6+21 x^5+61 x^4+17 x^3+15 x^2+46 x+66$
• $y^2=4 x^6+40 x^5+71 x^4+18 x^3+15 x^2+34 x+44$
• $y^2=32 x^6+33 x^5+8 x^4+22 x^3+15 x^2+63 x+7$
• $y^2=46 x^6+14 x^5+64 x^4+35 x^3+70 x^2+16 x+51$
• $y^2=39 x^6+62 x^5+43 x^4+53 x^3+11 x^2+54 x+2$
• $y^2=65 x^6+50 x^5+56 x^4+20 x^3+8 x^2+18 x+68$
• $y^2=30 x^6+33 x^5+x^4+77 x^3+12 x^2+68 x+55$
• $y^2=71 x^6+77 x^5+4 x^4+62 x^3+26 x^2+13$
• $y^2=18 x^6+65 x^5+x^4+5 x^3+47 x^2+48 x+31$
• $y^2=35 x^6+4 x^5+35 x^4+32 x^3+16 x^2+23 x+48$
• $y^2=72 x^6+33 x^5+50 x^4+26 x^3+44 x^2+30 x+23$
• $y^2=78 x^6+48 x^5+38 x^4+32 x^3+49 x^2+71 x+14$
• $y^2=22 x^6+62 x^5+21 x^4+70 x^3+22 x^2+27 x+48$
• $y^2=4 x^6+58 x^5+31 x^4+63 x^3+41 x^2+7 x+29$
• $y^2=15 x^6+68 x^5+32 x^4+52 x^3+25 x^2+39 x+75$
• $y^2=22 x^6+11 x^5+33 x^4+65 x^3+60 x^2+40 x+57$
• $y^2=32 x^6+38 x^5+16 x^4+31 x^3+7 x^2+57 x$
• $y^2=53 x^6+59 x^5+49 x^4+64 x^3+56 x^2+49 x+54$
• $y^2=24 x^6+41 x^5+44 x^4+56 x^3+73 x^2+29 x+9$
• $y^2=28 x^6+73 x^5+26 x^4+4 x^3+24 x^2+53 x+10$
• $y^2=4 x^6+43 x^5+32 x^4+51 x^3+26 x^2+16 x+41$
• $y^2=74 x^6+52 x^5+5 x^4+18 x^3+31 x^2+31 x+69$
• $y^2=23 x^6+39 x^5+17 x^4+68 x^3+24 x^2+9 x+28$
• $y^2=58 x^6+26 x^5+30 x^4+19 x^3+62 x^2+75 x+24$
• $y^2=29 x^6+8 x^5+37 x^4+28 x^3+38 x^2+5 x+61$
• $y^2=15 x^6+23 x^5+65 x^4+39 x^3+24 x^2+42 x+59$
• $y^2=63 x^6+13 x^5+54 x^4+55 x^2+57 x+10$
• $y^2=12 x^6+34 x^5+50 x^4+42 x^3+7 x^2+63 x+25$
• $y^2=74 x^5+24 x^4+28 x^3+37 x^2+71 x+12$
• $y^2=24 x^6+59 x^5+31 x^4+35 x^3+11 x^2+57 x+63$
• $y^2=74 x^6+49 x^5+43 x^4+59 x^3+11 x^2+50 x+69$
• $y^2=44 x^6+65 x^5+10 x^4+70 x^3+49 x^2+52 x+38$
• $y^2=55 x^6+68 x^5+x^4+8 x^3+18 x^2+70 x+71$
• $y^2=67 x^6+51 x^5+59 x^4+23 x^3+18 x^2+57 x+55$
• $y^2=51 x^6+59 x^5+47 x^4+53 x^3+41 x^2+41 x+53$
• $y^2=34 x^6+34 x^5+69 x^3+12 x^2+18 x+56$
• $y^2=77 x^6+48 x^5+71 x^4+60 x^3+72 x^2+30 x+27$
• $y^2=28 x^6+69 x^5+48 x^4+34 x^3+77 x^2+46 x+54$
• $y^2=17 x^6+31 x^5+14 x^4+8 x^3+60 x^2+70 x$
• $y^2=71 x^6+26 x^5+52 x^4+14 x^3+42 x^2+32 x+34$
• $y^2=25 x^6+58 x^5+72 x^4+7 x^3+62 x^2+26 x+46$
• $y^2=53 x^6+43 x^5+59 x^4+3 x^3+47 x^2+73 x+73$
• $y^2=18 x^6+55 x^5+60 x^4+33 x^3+19 x^2+69 x+31$
• $y^2=24 x^6+25 x^5+66 x^3+31 x^2+63 x+25$
• $y^2=12 x^6+48 x^5+54 x^4+40 x^3+44 x^2+18 x+8$
• $y^2=63 x^6+12 x^5+52 x^4+40 x^3+9 x^2+50 x+31$
• $y^2=69 x^5+41 x^4+53 x^3+64 x^2+56 x+23$
• $y^2=30 x^6+48 x^5+56 x^4+45 x^3+67 x^2+29 x+33$
• $y^2=61 x^6+39 x^5+60 x^4+15 x^3+12 x^2+8 x+65$
• $y^2=56 x^6+52 x^5+64 x^4+39 x^3+17 x^2+41 x+36$
• $y^2=76 x^6+66 x^5+75 x^4+72 x^3+48 x^2+53 x+44$
• $y^2=30 x^6+58 x^5+50 x^3+11 x^2+64 x+68$
• $y^2=20 x^6+55 x^5+63 x^4+49 x^3+9 x^2+19 x$
• $y^2=59 x^6+69 x^5+53 x^4+55 x^3+74 x^2+46 x+30$
• $y^2=21 x^6+5 x^5+46 x^4+16 x^3+8 x^2+2 x+30$
• $y^2=39 x^6+55 x^5+67 x^4+66 x^3+5 x^2+33 x+30$
• $y^2=30 x^6+54 x^5+24 x^4+8 x^3+74 x^2+11 x+60$
• $y^2=17 x^6+57 x^5+59 x^4+18 x^3+58 x^2+35 x+29$
• $y^2=55 x^6+67 x^5+16 x^4+63 x^3+37 x^2+31 x+8$
• $y^2=70 x^6+15 x^5+38 x^4+41 x^3+29 x^2+63 x+26$
• $y^2=63 x^6+14 x^5+14 x^4+5 x^3+49 x^2+62 x+23$
• $y^2=38 x^6+13 x^5+41 x^4+15 x^3+36 x^2+57 x+28$
• $y^2=53 x^6+5 x^5+4 x^4+25 x^3+16 x^2+10 x+27$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.aq $\times$ 1.79.af and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.79.aq : \(\Q(\sqrt{-15}) \).
• 1.79.af : \(\Q(\sqrt{-291}) \).

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_da	$2$	(not in LMFDB)
2.79.l_da	$2$	(not in LMFDB)
2.79.v_je	$2$	(not in LMFDB)