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

• Label: 2.67.u_iy
• 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:	$1 + 20 x + 232 x^{2} + 1340 x^{3} + 4489 x^{4}$
Frobenius angles:	$\pm0.675732907495$, $\pm0.745586176039$
Angle rank:	$2$ (numerical)
Number field:	4.0.1712384.2
Galois group:	$D_{4}$
Jacobians:	$16$
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6082$	$20447684$	$89888414194$	$406356088015376$	$1822809588318433282$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$88$	$4554$	$298864$	$20165430$	$1350104208$	$90457739418$	$6060718665544$	$406067649248094$	$27206534279602648$	$1822837806877809514$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=25 x^6+31 x^5+58 x^4+3 x^3+60 x^2+57 x+38$
• $y^2=26 x^6+10 x^5+27 x^4+19 x^3+7 x^2+27 x+19$
• $y^2=49 x^6+x^5+12 x^4+40 x^3+46 x^2+63 x+15$
• $y^2=62 x^6+45 x^5+x^4+58 x^3+50 x^2+3 x+8$
• $y^2=59 x^6+53 x^5+34 x^4+16 x^3+45 x^2+26 x+58$
• $y^2=21 x^6+23 x^5+3 x^4+63 x^3+66 x^2+44 x+16$
• $y^2=55 x^6+34 x^5+27 x^4+3 x^3+59 x^2+40 x+43$
• $y^2=32 x^6+42 x^5+28 x^4+24 x^3+10 x^2+22 x+19$
• $y^2=44 x^6+13 x^5+43 x^4+16 x^3+56 x^2+65 x+18$
• $y^2=39 x^6+54 x^5+13 x^4+37 x^3+14 x^2+64 x+10$
• $y^2=35 x^6+60 x^5+57 x^4+44 x^3+30 x^2+58 x+63$
• $y^2=47 x^6+26 x^5+2 x^4+52 x^3+63 x^2+17 x+19$
• $y^2=37 x^6+54 x^5+35 x^4+33 x^3+47 x^2+61 x+55$
• $y^2=49 x^6+21 x^5+59 x^4+47 x^3+23 x^2+51 x+17$
• $y^2=7 x^6+15 x^5+21 x^4+42 x^3+23 x^2+63 x+56$
• $y^2=50 x^6+32 x^5+25 x^4+55 x^3+24 x^2+5 x+29$

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 4.0.1712384.2.

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.au_iy	$2$	(not in LMFDB)