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

• Label: 2.79.u_jy
• 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:	$( 1 + 10 x + 79 x^{2} )^{2}$
	$1 + 20 x + 258 x^{2} + 1580 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.690177289346$, $\pm0.690177289346$
Angle rank:	$1$ (numerical)
Jacobians:	$87$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8100$	$39690000$	$241739388900$	$1517819264640000$	$9468381016694902500$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$100$	$6358$	$490300$	$38968318$	$3077090500$	$243085673878$	$19203924108700$	$1517108799431038$	$119851594892692900$	$9468276094353667798$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 87 curves (of which all are hyperelliptic):

• $y^2=36 x^6+67 x^5+10 x^4+56 x^3+16 x^2+23 x+16$
• $y^2=25 x^6+52 x^5+63 x^4+36 x^3+60 x^2+61 x+66$
• $y^2=67 x^6+9 x^5+33 x^4+47 x^3+66 x^2+11 x+1$
• $y^2=2 x^6+58 x^5+12 x^4+40 x^3+31 x^2+11 x+4$
• $y^2=8 x^6+8 x^5+3 x^4+75 x^3+25 x^2+40 x+72$
• $y^2=x^6+x^3+38$
• $y^2=66 x^6+33 x^5+37 x^4+32 x^3+39 x^2+74 x+77$
• $y^2=10 x^6+12 x^5+27 x^4+26 x^3+6 x^2+39 x+70$
• $y^2=32 x^6+44 x^5+42 x^4+32 x^3+42 x^2+44 x+32$
• $y^2=42 x^6+73 x^5+48 x^4+18 x^3+48 x^2+73 x+42$
• $y^2=56 x^6+17 x^5+39 x^4+54 x^3+39 x^2+17 x+56$
• $y^2=11 x^6+50 x^5+40 x^4+23 x^3+40 x^2+50 x+11$
• $y^2=48 x^6+24 x^4+49 x^3+24 x^2+48$
• $y^2=75 x^6+9 x^5+72 x^4+34 x^3+33 x^2+67 x+58$
• $y^2=x^6+5 x^3+46$
• $y^2=28 x^6+63 x^5+18 x^4+47 x^3+52 x^2+14 x+23$
• $y^2=31 x^6+62 x^5+23 x^4+66 x^3+44 x^2+2 x+50$
• $y^2=7 x^6+30 x^5+14 x^4+38 x^3+14 x^2+30 x+7$
• $y^2=31 x^6+74 x^5+31 x^4+10 x^3+40 x^2+75 x+9$
• $y^2=23 x^6+32 x^5+30 x^4+40 x^3+42 x^2+37 x+23$
• and

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.k^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-6}) \)$)$

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.au_jy	$2$	(not in LMFDB)
2.79.a_cg	$2$	(not in LMFDB)
2.79.ak_v	$3$	(not in LMFDB)