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

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

Invariants

Base field:	$\F_{79}$
Dimension:	$2$
L-polynomial:	$1 - 28 x + 348 x^{2} - 2212 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.123766042460$, $\pm0.274866475067$
Angle rank:	$2$ (numerical)
Number field:	4.0.4776192.1
Galois group:	$D_{4}$
Jacobians:	$20$

This isogeny class is simple and 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4350$	$38410500$	$243405298350$	$1517563978266000$	$9468531892360116750$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$52$	$6154$	$493684$	$38961766$	$3077139532$	$243087690922$	$19203908473228$	$1517108824593406$	$119851596574228276$	$9468276091477167274$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which all are hyperelliptic):

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The endomorphism algebra of this simple isogeny class is 4.0.4776192.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.79.bc_nk	$2$	(not in LMFDB)