Abelian variety isogeny class 2.67.e_fb over $\F_{67}$

• Label: 2.67.e_fb
• Base field: $\F_{67}$
• 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:	$\F_{67}$
Dimension:	$2$
L-polynomial:	$1 + 4 x + 131 x^{2} + 268 x^{3} + 4489 x^{4}$
Frobenius angles:	$\pm0.487440836490$, $\pm0.591590009502$
Angle rank:	$2$ (numerical)
Number field:	4.0.51694608.1
Galois group:	$D_{4}$
Jacobians:	$40$
Isomorphism classes:	40

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4893$	$21279657$	$90247137876$	$405815337352089$	$1822916712914539053$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$72$	$4736$	$300060$	$20138596$	$1350183552$	$90458873678$	$6060708500352$	$406067666155204$	$27206534454572772$	$1822837804437991616$

Jacobians and polarizations

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

• $y^2=26 x^6+23 x^5+44 x^4+58 x^3+64 x^2+8 x+27$
• $y^2=14 x^6+38 x^5+13 x^4+38 x^3+26 x^2+60 x+17$
• $y^2=48 x^6+50 x^5+64 x^4+28 x^3+64 x^2+17 x+37$
• $y^2=28 x^6+29 x^5+7 x^4+28 x^3+28 x^2+18 x+23$
• $y^2=65 x^6+14 x^5+12 x^4+51 x^3+32 x^2+49 x+17$
• $y^2=17 x^6+44 x^5+54 x^4+53 x^3+16 x^2+34 x+62$
• $y^2=25 x^6+55 x^5+32 x^4+62 x^3+60 x^2+36 x+37$
• $y^2=56 x^6+8 x^5+65 x^4+13 x^3+63 x^2+9 x+16$
• $y^2=20 x^6+4 x^5+54 x^4+18 x^3+47 x^2+43 x+46$
• $y^2=14 x^6+64 x^5+51 x^4+26 x^3+6 x^2+36 x+10$
• $y^2=39 x^6+10 x^5+46 x^4+9 x^3+64 x^2+47 x+44$
• $y^2=32 x^6+51 x^5+2 x^4+46 x^3+47 x^2+41 x+62$
• $y^2=31 x^6+30 x^5+32 x^4+55 x^3+44 x^2+45 x+62$
• $y^2=65 x^6+46 x^5+47 x^4+43 x^3+23 x^2+56 x+38$
• $y^2=28 x^6+65 x^5+28 x^4+11 x^3+29 x^2+6 x+40$
• $y^2=18 x^6+33 x^5+25 x^4+65 x^3+62 x^2+24 x+30$
• $y^2=51 x^6+42 x^5+12 x^4+10 x^3+66 x^2+37 x+48$
• $y^2=29 x^6+3 x^5+12 x^4+39 x^3+42 x^2+48 x+37$
• $y^2=29 x^6+15 x^5+3 x^3+2 x^2+24 x+9$
• $y^2=40 x^6+20 x^5+20 x^4+20 x^3+49 x^2+51 x+30$
• and

• $y^2=9 x^6+11 x^5+56 x^4+35 x^3+59 x^2+46 x+51$
• $y^2=36 x^6+x^5+11 x^4+23 x^3+42 x^2+11 x+6$
• $y^2=29 x^6+x^5+30 x^4+36 x^3+x^2+23 x+6$
• $y^2=3 x^6+29 x^5+6 x^4+21 x^3+59 x^2+65 x+19$
• $y^2=46 x^6+22 x^5+21 x^4+50 x^3+5 x^2+49 x+18$
• $y^2=33 x^6+38 x^5+19 x^4+66 x^3+28 x^2+7 x+29$
• $y^2=3 x^6+8 x^5+18 x^4+20 x^3+49 x^2+2 x+51$
• $y^2=18 x^6+4 x^5+63 x^4+38 x^3+33 x^2+57 x+13$
• $y^2=14 x^6+35 x^5+33 x^4+55 x^3+63 x^2+25 x+58$
• $y^2=43 x^6+61 x^5+28 x^4+47 x^3+22 x^2+22 x+54$
• $y^2=8 x^6+19 x^5+7 x^4+61 x^3+18 x^2+66 x+31$
• $y^2=57 x^6+8 x^5+20 x^4+66 x^3+13 x^2+51 x+65$
• $y^2=54 x^6+41 x^5+65 x^4+61 x^3+8 x^2+37 x+66$
• $y^2=19 x^6+57 x^5+23 x^4+16 x^3+2 x^2+64 x+49$
• $y^2=38 x^6+18 x^5+9 x^4+11 x^3+22 x^2+29 x+25$
• $y^2=21 x^6+63 x^5+17 x^4+62 x^3+57 x^2+47 x+62$
• $y^2=30 x^6+63 x^5+54 x^4+31 x^3+11 x^2+54 x+17$
• $y^2=21 x^6+59 x^5+42 x^4+46 x^3+37 x^2+58 x+23$
• $y^2=65 x^6+18 x^5+25 x^4+59 x^3+35 x^2+58 x+42$
• $y^2=3 x^6+5 x^5+27 x^4+44 x^3+34 x^2+40 x+31$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{67}$.

Endomorphism algebra over $\F_{67}$

The endomorphism algebra of this simple isogeny class is 4.0.51694608.1.

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
2.67.ae_fb	$2$	(not in LMFDB)