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

• Label: 2.79.b_ada
• 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:	$1 + x - 78 x^{2} + 79 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.184582454493$, $\pm0.851249121159$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}, \sqrt{-35})\)
Galois group:	$C_2^2$
Jacobians:	$82$
Cyclic group of points:	no
Non-cyclic primes:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6244$	$37988496$	$243321212176$	$1517582824640064$	$9468370887683848924$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$81$	$6085$	$493512$	$38962249$	$3077087211$	$243089316286$	$19203905621709$	$1517108880042289$	$119851595310763608$	$9468276077422052125$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 82 curves (of which all are hyperelliptic):

• $y^2=41 x^6+5 x^5+16 x^4+33 x^3+13 x^2+61 x+9$
• $y^2=77 x^6+21 x^5+69 x^4+3 x^3+14 x^2+8 x+24$
• $y^2=69 x^6+2 x^5+10 x^4+8 x^3+34 x^2+25 x$
• $y^2=38 x^6+2 x^5+31 x^4+45 x^3+17 x^2+27 x+49$
• $y^2=3 x^6+3 x^3+53$
• $y^2=48 x^6+31 x^5+8 x^4+17 x^3+66 x^2+76 x+30$
• $y^2=64 x^6+45 x^5+11 x^4+73 x^3+69 x^2+3 x+63$
• $y^2=3 x^6+68 x^5+36 x^4+13 x^3+33 x^2+68 x+66$
• $y^2=3 x^6+74 x^5+48 x^4+34 x^3+17 x^2+78 x+6$
• $y^2=63 x^6+3 x^5+27 x^4+32 x^3+36 x^2+37 x+25$
• $y^2=9 x^6+27 x^5+53 x^4+47 x^3+32 x^2+46 x+65$
• $y^2=47 x^6+36 x^5+71 x^4+24 x^3+64 x^2+17 x+29$
• $y^2=39 x^6+33 x^5+78 x^4+11 x^3+14 x^2+5 x+23$
• $y^2=71 x^6+7 x^5+13 x^4+60 x^3+71 x^2+67 x+55$
• $y^2=5 x^6+41 x^5+61 x^4+18 x^3+38 x^2+2 x+45$
• $y^2=48 x^6+31 x^5+48 x^4+2 x^3+75 x^2+74 x+76$
• $y^2=47 x^6+38 x^5+30 x^4+78 x^3+60 x^2+52 x+65$
• $y^2=71 x^6+73 x^5+14 x^4+78 x^3+67 x^2+56 x+25$
• $y^2=26 x^6+16 x^5+6 x^4+40 x^3+45 x^2+21 x+74$
• $y^2=70 x^5+69 x^4+6 x^3+43 x^2+36 x+59$
• and

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

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 \(\Q(\sqrt{-3}, \sqrt{-35})\).

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

The base change of $A$ to $\F_{79^{3}}$ is 1.493039.jc^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-35}) \)$)$

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.ab_ada	$2$	(not in LMFDB)
2.79.ac_gd	$3$	(not in LMFDB)
2.79.ab_ada	$6$	(not in LMFDB)