Abelian variety isogeny class 2.127.abm_xo over $\F_{127}$

• Label: 2.127.abm_xo
• Base field: $\F_{127}$
• 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:	$\F_{127}$
Dimension:	$2$
L-polynomial:	$1 - 38 x + 612 x^{2} - 4826 x^{3} + 16129 x^{4}$
Frobenius angles:	$\pm0.128321556909$, $\pm0.222174226426$
Angle rank:	$2$ (numerical)
Number field:	4.0.2362176.1
Galois group:	$D_{4}$
Jacobians:	$16$
Isomorphism classes:	16

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$11878$	$256636068$	$4196731788574$	$67683468900310224$	$1091550310992340263118$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$15910$	$2048802$	$260176294$	$33038867550$	$4195878038710$	$532875896025990$	$67675234361335294$	$8594754747928792314$	$1091533853064314262550$

Jacobians and polarizations

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

• $y^2=125x^6+124x^5+8x^4+39x^3+60x^2+35x+106$
• $y^2=109x^6+23x^5+105x^4+117x^3+72x^2+67x+69$
• $y^2=6x^6+71x^5+65x^4+57x^3+93x^2+49x+59$
• $y^2=53x^6+95x^5+17x^4+7x^3+66x^2+47x+125$
• $y^2=58x^6+120x^5+12x^4+12x^3+70x^2+17x+99$
• $y^2=93x^6+31x^5+50x^4+30x^3+18x^2+108x+63$
• $y^2=9x^6+85x^5+20x^4+62x^3+84x^2+103x+115$
• $y^2=11x^6+35x^5+72x^4+60x^3+92x^2+x+69$
• $y^2=4x^6+117x^5+115x^4+119x^3+83x^2+2x+51$
• $y^2=125x^6+60x^5+41x^4+89x^3+12x^2+109x+10$
• $y^2=53x^6+76x^5+33x^4+10x^3+109x^2+41x+46$
• $y^2=116x^6+68x^5+29x^4+124x^3+85x^2+47x+93$
• $y^2=8x^6+56x^5+126x^4+112x^3+15x^2+57x+74$
• $y^2=75x^6+15x^5+95x^4+80x^3+114x^2+18x+38$
• $y^2=120x^6+25x^5+93x^4+111x^3+48x^2+2x+100$
• $y^2=122x^6+79x^5+104x^4+28x^3+121x^2+36x+7$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{127}$.

Endomorphism algebra over $\F_{127}$

The endomorphism algebra of this simple isogeny class is 4.0.2362176.1.

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
2.127.bm_xo	$2$	(not in LMFDB)