Abelian variety isogeny class 2.71.abb_mh over $\F_{71}$

• Label: 2.71.abb_mh
• Base field: $\F_{71}$
• 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:	$\F_{71}$
Dimension:	$2$
L-polynomial:	$1 - 27 x + 319 x^{2} - 1917 x^{3} + 5041 x^{4}$
Frobenius angles:	$\pm0.113553616906$, $\pm0.268382636419$
Angle rank:	$2$ (numerical)
Number field:	4.0.2418885.1
Galois group:	$D_{4}$
Jacobians:	$14$
Isomorphism classes:	14

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3417$	$24961185$	$128245391775$	$645966238252365$	$3255348972857499312$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$45$	$4951$	$358317$	$25420051$	$1804287780$	$128100426883$	$9095119381575$	$645753534485491$	$45848501033247027$	$3255243556266128926$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=62x^6+24x^5+20x^4+49x^3+43x^2+22x+11$
• $y^2=54x^6+66x^5+36x^4+49x^3+68x^2+57x+4$
• $y^2=41x^6+44x^5+25x^4+38x^3+17x^2+67x+60$
• $y^2=22x^6+16x^5+3x^4+57x^3+2x^2+51x+2$
• $y^2=24x^6+58x^5+21x^4+18x^3+12x^2+36x+1$
• $y^2=13x^6+66x^5+59x^4+38x^3+33x^2+50x+31$
• $y^2=35x^6+26x^5+40x^4+33x^3+55x^2+19x+2$
• $y^2=53x^6+20x^5+27x^4+46x^3+60x^2+58x+43$
• $y^2=47x^6+32x^5+58x^4+27x^3+38x^2+51x+19$
• $y^2=51x^6+41x^5+53x^4+48x^3+30x^2+29x+14$
• $y^2=63x^6+3x^5+27x^4+32x^3+15x^2+48x+59$
• $y^2=28x^6+47x^5+60x^4+48x^3+45x^2+42x+32$
• $y^2=64x^6+70x^5+35x^4+68x^3+46x^2+27x+37$
• $y^2=39x^6+13x^5+51x^4+49x^3+41x^2+52x+51$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{71}$.

Endomorphism algebra over $\F_{71}$

The endomorphism algebra of this simple isogeny class is 4.0.2418885.1.

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
2.71.bb_mh	$2$	(not in LMFDB)