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

• Label: 2.79.abc_nj
• 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:	$1 - 28 x + 347 x^{2} - 2212 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.114139050386$, $\pm0.279461582628$
Angle rank:	$2$ (numerical)
Number field:	4.0.634256.1
Galois group:	$D_{4}$
Jacobians:	$18$
Isomorphism classes:	18

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4349$	$38397321$	$243363725252$	$1517495953959801$	$9468459519126656549$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$52$	$6152$	$493600$	$38960020$	$3077116012$	$243087476582$	$19203907378372$	$1517108827419364$	$119851596705425440$	$9468276093100641752$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which all are hyperelliptic):

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

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 4.0.634256.1.

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_nj	$2$	(not in LMFDB)