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

• Label: 2.79.w_kt
• 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:	$( 1 + 11 x + 79 x^{2} )^{2}$
	$1 + 22 x + 279 x^{2} + 1738 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.712380201669$, $\pm0.712380201669$
Angle rank:	$1$ (numerical)
Jacobians:	$40$
Cyclic group of points:	no
Non-cyclic primes:	$7, 13$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8281$	$39425841$	$241831831696$	$1517974715828025$	$9468144151216271521$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$102$	$6316$	$490488$	$38972308$	$3077013522$	$243086171326$	$19203926499678$	$1517108718709348$	$119851595602219752$	$9468276094015811356$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 40 curves (of which all are hyperelliptic):

• $y^2=10 x^6+32 x^5+70 x^4+75 x^3+47 x^2+55 x+28$
• $y^2=9 x^6+31 x^5+26 x^4+55 x^3+36 x^2+47 x+31$
• $y^2=21 x^6+12 x^5+15 x^4+22 x^3+72 x^2+49 x+22$
• $y^2=31 x^6+60 x^5+35 x^4+78 x^3+75 x^2+42 x+27$
• $y^2=35 x^6+3 x^5+21 x^4+64 x^3+21 x^2+3 x+35$
• $y^2=10 x^6+12 x^5+67 x^4+18 x^3+67 x^2+12 x+10$
• $y^2=74 x^6+13 x^5+74 x^4+76 x^3+74 x^2+13 x+74$
• $y^2=18 x^6+68 x^5+40 x^4+38 x^3+40 x^2+68 x+18$
• $y^2=39 x^6+40 x^5+53 x^4+45 x^3+53 x^2+40 x+39$
• $y^2=71 x^6+24 x^5+71 x^3+21 x^2+42 x+46$
• $y^2=14 x^6+34 x^5+5 x^4+36 x^3+5 x^2+34 x+14$
• $y^2=24 x^6+17 x^5+47 x^4+44 x^3+13 x^2+14 x+26$
• $y^2=10 x^6+35 x^5+14 x^4+59 x^3+14 x^2+35 x+10$
• $y^2=67 x^6+39 x^5+50 x^4+20 x^3+25 x^2+14 x+58$
• $y^2=6 x^6+9 x^5+59 x^3+9 x+6$
• $y^2=67 x^6+11 x^5+20 x^4+4 x^3+17 x^2+55 x+3$
• $y^2=32 x^6+30 x^5+49 x^4+60 x^3+41 x^2+18 x+32$
• $y^2=55 x^6+73 x^5+18 x^4+54 x^3+18 x^2+73 x+55$
• $y^2=68 x^6+38 x^5+2 x^4+72 x^3+44 x^2+32 x+55$
• $y^2=33 x^6+71 x^5+57 x^4+18 x^3+57 x^2+71 x+33$
• and

• $y^2=48 x^6+54 x^5+14 x^4+13 x^3+64 x^2+8 x+11$
• $y^2=72 x^6+59 x^5+68 x^4+71 x^3+32 x^2+71 x+39$
• $y^2=52 x^6+26 x^5+54 x^4+40 x^3+43 x^2+8 x+52$
• $y^2=76 x^6+23 x^5+67 x^4+26 x^3+67 x^2+23 x+76$
• $y^2=11 x^6+4 x^5+50 x^4+65 x^3+50 x^2+4 x+11$
• $y^2=9 x^6+66 x^5+59 x^4+32 x^3+59 x^2+66 x+9$
• $y^2=19 x^6+2 x^5+40 x^4+70 x^3+40 x^2+2 x+19$
• $y^2=60 x^6+54 x^5+64 x^4+38 x^3+64 x^2+54 x+60$
• $y^2=3 x^6+69 x^3+3$
• $y^2=25 x^6+11 x^5+43 x^4+31 x^3+43 x^2+69 x+37$
• $y^2=24 x^6+40 x^5+47 x^4+44 x^3+47 x^2+40 x+24$
• $y^2=19 x^6+14 x^5+61 x^4+55 x^3+29 x^2+5 x+16$
• $y^2=20 x^6+x^5+75 x^4+14 x^2+56 x+37$
• $y^2=50 x^6+47 x^5+36 x^4+28 x^3+36 x^2+47 x+50$
• $y^2=29 x^6+60 x^5+2 x^4+36 x^3+2 x^2+60 x+29$
• $y^2=59 x^6+6 x^5+64 x^4+54 x^3+74 x^2+48 x+4$
• $y^2=3 x^6+3 x^3+3$
• $y^2=11 x^6+59 x^5+58 x^4+46 x^3+19 x^2+40 x+5$
• $y^2=61 x^6+51 x^5+29 x^3+51 x+61$
• $y^2=50 x^6+69 x^5+39 x^4+44 x^3+39 x^2+69 x+50$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.l^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-195}) \)$)$

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.aw_kt	$2$	(not in LMFDB)
2.79.a_bl	$2$	(not in LMFDB)
2.79.al_bq	$3$	(not in LMFDB)