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

• Label: 2.67.m_go
• Base field: $\F_{67}$
• 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:	$\F_{67}$
Dimension:	$2$
L-polynomial:	$( 1 + 6 x + 67 x^{2} )^{2}$
	$1 + 12 x + 170 x^{2} + 804 x^{3} + 4489 x^{4}$
Frobenius angles:	$\pm0.619446875636$, $\pm0.619446875636$
Angle rank:	$1$ (numerical)
Jacobians:	$20$
Cyclic group of points:	no
Non-cyclic primes:	$2, 37$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$5476$	$21049744$	$89864451076$	$406042489046016$	$1823027061900697636$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$80$	$4686$	$298784$	$20149870$	$1350265280$	$90457625022$	$6060706756688$	$406067757377374$	$27206534242229168$	$1822837800128167086$

Jacobians and polarizations

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

• $y^2=6 x^6+23 x^5+17 x^4+64 x^3+17 x^2+23 x+6$
• $y^2=33 x^6+18 x^5+36 x^4+38 x^3+4 x^2+13 x+9$
• $y^2=62 x^6+53 x^5+51 x^4+25 x^3+7 x^2+9 x+43$
• $y^2=3 x^6+6 x^5+33 x^4+32 x^3+30 x^2+27 x+44$
• $y^2=28 x^6+65 x^5+62 x^4+66 x^3+51 x^2+20 x+47$
• $y^2=11 x^6+34 x^5+15 x^4+61 x^3+28 x^2+30 x+13$
• $y^2=52 x^6+15 x^5+50 x^4+39 x^3+26 x^2+5 x+52$
• $y^2=56 x^6+4 x^5+37 x^4+17 x^3+45 x^2+65 x+12$
• $y^2=41 x^6+11 x^4+56 x^3+57 x^2+35 x+41$
• $y^2=8 x^6+37 x^5+27 x^4+23 x^3+14 x^2+4 x$
• $y^2=23 x^6+35 x^4+35 x^2+23$
• $y^2=32 x^6+43 x^5+53 x^4+25 x^3+40 x^2+60 x+16$
• $y^2=15 x^6+35 x^5+20 x^4+57 x^3+10 x^2+36 x+48$
• $y^2=38 x^6+9 x^5+58 x^4+5 x^3+10 x^2+17 x+63$
• $y^2=28 x^6+55 x^5+56 x^4+56 x^3+33 x^2+15 x+42$
• $y^2=43 x^6+16 x^5+35 x^4+66 x^3+56 x^2+9 x+19$
• $y^2=57 x^5+23 x^4+59 x^3+37 x^2+25 x+2$
• $y^2=x^6+51 x^5+9 x^4+28 x^3+49 x^2+3 x+59$
• $y^2=4 x^6+56 x^5+51 x^4+x^3+4 x^2+56 x+49$
• $y^2=54 x^6+17 x^4+32 x^3+49 x^2+54 x+56$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{67}$

The isogeny class factors as 1.67.g^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-58}) \)$)$

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
2.67.am_go	$2$	(not in LMFDB)
2.67.a_du	$2$	(not in LMFDB)
2.67.ag_abf	$3$	(not in LMFDB)