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

• Label: 2.79.a_ef
• 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:	$( 1 - 7 x + 79 x^{2} )( 1 + 7 x + 79 x^{2} )$
	$1 + 109 x^{2} + 6241 x^{4}$
Frobenius angles:	$\pm0.371166915609$, $\pm0.628833084391$
Angle rank:	$1$ (numerical)
Jacobians:	$66$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6351$	$40335201$	$243086709744$	$1517155706166489$	$9468276078829500951$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$80$	$6460$	$493040$	$38951284$	$3077056400$	$243085963966$	$19203908986160$	$1517108964984484$	$119851595982618320$	$9468276075032154700$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 66 curves (of which all are hyperelliptic):

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

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{79^{2}}$.

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.ah $\times$ 1.79.h 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.ah : \(\Q(\sqrt{-267}) \).
• 1.79.h : \(\Q(\sqrt{-267}) \).

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

The base change of $A$ to $\F_{79^{2}}$ is 1.6241.ef^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-267}) \)$)$

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.ao_hz	$2$	(not in LMFDB)
2.79.o_hz	$2$	(not in LMFDB)
2.79.a_aef	$4$	(not in LMFDB)