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

• Label: 2.79.az_li
• 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:	$( 1 - 17 x + 79 x^{2} )( 1 - 8 x + 79 x^{2} )$
	$1 - 25 x + 294 x^{2} - 1975 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.0944227114288$, $\pm0.351411445414$
Angle rank:	$2$ (numerical)
Jacobians:	$56$
Cyclic group of points:	no
Non-cyclic primes:	$2, 3$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4536$	$38719296$	$243333738144$	$1517068635312384$	$9467999539115200776$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$55$	$6205$	$493540$	$38949049$	$3076966525$	$243086730766$	$19203912129835$	$1517108930520529$	$119851597203243820$	$9468276088413938725$

Jacobians and polarizations

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

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

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.ar $\times$ 1.79.ai 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.ar : \(\Q(\sqrt{-3}) \).
• 1.79.ai : \(\Q(\sqrt{-7}) \).

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.aj_w	$2$	(not in LMFDB)
2.79.j_w	$2$	(not in LMFDB)
2.79.z_li	$2$	(not in LMFDB)
2.79.ae_ew	$3$	(not in LMFDB)
2.79.f_cc	$3$	(not in LMFDB)