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

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

Invariants

Base field:	$\F_{79}$
Dimension:	$2$
L-polynomial:	$1 + 5 x - 54 x^{2} + 395 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.257422971303$, $\pm0.924089637970$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}, \sqrt{97})\)
Galois group:	$C_2^2$
Jacobians:	$72$
Cyclic group of points:	no
Non-cyclic primes:	$2, 3$

This isogeny class is simple but not geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6588$	$38131344$	$244134810000$	$1517311611146304$	$9468613875466651428$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$85$	$6109$	$495160$	$38955289$	$3077166175$	$243087180478$	$19203901001545$	$1517108759119249$	$119851595228922280$	$9468276088523285029$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 72 curves (of which all are hyperelliptic):

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

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{79^{3}}$.

Endomorphism algebra over $\F_{79}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}, \sqrt{97})\).

Endomorphism algebra over $\overline{\F}_{79}$

The base change of $A$ to $\F_{79^{3}}$ is 1.493039.bou^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.af_acc	$2$	(not in LMFDB)
2.79.ak_hb	$3$	(not in LMFDB)
2.79.a_fd	$6$	(not in LMFDB)