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

• Label: 2.79.k_hb
• 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:	$( 1 + 5 x + 79 x^{2} )^{2}$
	$1 + 10 x + 183 x^{2} + 790 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.590756304637$, $\pm0.590756304637$
Angle rank:	$1$ (numerical)
Jacobians:	$56$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7225$	$40640625$	$242044320400$	$1516703288765625$	$9468951668564130625$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$6508$	$490920$	$38939668$	$3077275950$	$243087180478$	$19203893016930$	$1517108911481188$	$119851596736314360$	$9468276070833971548$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 56 curves (of which all are hyperelliptic):

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

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.f^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-291}) \)$)$

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.ak_hb	$2$	(not in LMFDB)
2.79.a_fd	$2$	(not in LMFDB)
2.79.af_acc	$3$	(not in LMFDB)