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

• Label: 2.107.abi_sy
• 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:	$1 - 34 x + 492 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.0604166695618$, $\pm0.269957969854$
Angle rank:	$2$ (numerical)
Number field:	4.0.7101248.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8270$	$129127780$	$1500687737990$	$17182592067592400$	$196714710853131425350$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11278$	$1225010$	$131085174$	$14025487014$	$1500728425966$	$160578117732638$	$17181861554733726$	$1838459212196999690$	$196715135754431249118$

Jacobians and polarizations

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

• $y^2=50x^6+79x^5+2x^4+99x^3+67x^2+51x+55$
• $y^2=77x^6+94x^5+71x^4+102x^3+28x^2+24x+98$
• $y^2=16x^6+73x^5+75x^4+47x^3+33x^2+51x+7$
• $y^2=91x^6+81x^5+56x^4+90x^3+8x^2+18x+72$
• $y^2=77x^6+12x^5+52x^4+85x^3+76x^2+60x+26$
• $y^2=98x^6+37x^5+44x^4+72x^3+2x^2+60x+68$
• $y^2=23x^5+11x^4+104x^3+17x^2+22x+80$
• $y^2=78x^6+9x^5+85x^4+15x^3+86x^2+85x+73$
• $y^2=91x^6+50x^5+52x^4+81x^3+51x^2+24x+45$
• $y^2=87x^6+65x^5+78x^4+41x^3+37x^2+77x+106$
• $y^2=77x^6+98x^5+31x^4+102x^3+95x^2+52x+87$
• $y^2=92x^6+75x^5+75x^4+6x^3+22x^2+42x+26$
• $y^2=27x^6+42x^5+88x^4+43x^3+60x^2+8x+11$
• $y^2=60x^6+66x^5+80x^4+80x^3+105x^2+75x+60$
• $y^2=55x^6+3x^5+40x^4+99x^3+57x^2+87x+75$
• $y^2=87x^6+2x^5+104x^4+61x^3+97x^2+34x+18$

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 4.0.7101248.1.

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
2.107.bi_sy	$2$	(not in LMFDB)