Abelian variety isogeny class 2.107.abh_sd over $\F_{107}$

• Label: 2.107.abh_sd
• Base field: $\F_{107}$
• 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:	$\F_{107}$
Dimension:	$2$
L-polynomial:	$1 - 33 x + 471 x^{2} - 3531 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.0527134479232$, $\pm0.291652687618$
Angle rank:	$2$ (numerical)
Number field:	4.0.11657893.2
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8357$	$129408145$	$1500850101647$	$17182094630854525$	$196713323262495970352$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$75$	$11303$	$1225143$	$131081379$	$14025388080$	$1500727282931$	$160578112381041$	$17181861603326611$	$1838459213239241601$	$196715135758436888918$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=42x^6+101x^5+28x^4+20x^3+71x^2+30x+26$
• $y^2=98x^6+88x^5+99x^4+62x^3+96x^2+46x+30$
• $y^2=84x^6+50x^5+86x^4+76x^3+106x^2+54x+51$
• $y^2=77x^6+51x^5+85x^4+18x^3+3x^2+81x+82$
• $y^2=51x^6+57x^5+94x^4+64x^3+72x^2+68x+42$
• $y^2=35x^6+45x^5+30x^4+94x^3+13x^2+66x+71$
• $y^2=82x^6+x^5+86x^4+98x^3+72x^2+91x+54$
• $y^2=72x^6+59x^5+46x^4+34x^3+60x^2+86x+93$
• $y^2=82x^6+17x^5+25x^4+5x^3+27x^2+104x+24$
• $y^2=93x^6+46x^5+68x^4+32x^3+87x^2+8x+8$
• $y^2=59x^6+95x^5+55x^4+30x^3+55x^2+3x+46$
• $y^2=22x^6+57x^5+41x^4+93x^3+87x^2+43x+33$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{107}$.

Endomorphism algebra over $\F_{107}$

The endomorphism algebra of this simple isogeny class is 4.0.11657893.2.

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
2.107.bh_sd	$2$	(not in LMFDB)