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

• Label: 2.127.abm_xl
• 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:	$1 - 38 x + 609 x^{2} - 4826 x^{3} + 16129 x^{4}$
Frobenius angles:	$\pm0.0993690084490$, $\pm0.237505795395$
Angle rank:	$2$ (numerical)
Number field:	4.0.6460992.1
Galois group:	$D_{4}$
Jacobians:	$20$
Isomorphism classes:	20

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$11875$	$256535625$	$4196029682500$	$67680866567465625$	$1091543719783097996875$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$15904$	$2048460$	$260166292$	$33038668050$	$4195875090166$	$532875864217710$	$67675234162191268$	$8594754748828205460$	$1091533853114181930064$

Jacobians and polarizations

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

• $y^2=70x^6+69x^5+116x^4+118x^3+40x^2+9x+5$
• $y^2=94x^6+40x^5+105x^4+95x^3+104x^2+80x+114$
• $y^2=85x^6+115x^5+111x^4+122x^3+86x^2+17x+20$
• $y^2=14x^6+101x^5+31x^4+38x^3+121x^2+26x+26$
• $y^2=89x^6+115x^5+50x^4+113x^3+67x^2+86x+84$
• $y^2=100x^6+35x^5+50x^4+108x^3+50x^2+94x+28$
• $y^2=100x^6+26x^5+57x^4+46x^3+5x^2+68x+16$
• $y^2=43x^6+20x^5+51x^4+74x^3+16x^2+117x+118$
• $y^2=66x^6+66x^5+12x^4+90x^3+109x^2+81x+102$
• $y^2=54x^6+97x^5+122x^4+5x^3+84x^2+47x+12$
• $y^2=108x^6+90x^5+36x^4+63x^2+113x+50$
• $y^2=102x^6+112x^5+71x^4+88x^3+38x^2+111$
• $y^2=74x^6+77x^5+90x^4+105x^3+42x^2+122x+123$
• $y^2=83x^6+14x^5+17x^4+117x^3+52x^2+92x+24$
• $y^2=12x^6+24x^5+120x^4+68x^3+28x^2+74x+23$
• $y^2=19x^6+43x^5+98x^4+2x^3+38x^2+39x+54$
• $y^2=7x^6+57x^5+33x^4+125x^3+108x^2+24x+22$
• $y^2=33x^6+78x^5+25x^4+27x^3+52x^2+37x+5$
• $y^2=80x^6+124x^5+41x^4+38x^3+98x^2+11x+65$
• $y^2=39x^6+98x^5+60x^4+6x^3+17x^2+125x+57$

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 4.0.6460992.1.

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_xl	$2$	(not in LMFDB)