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

• Label: 2.107.abi_ti
• Base field: $\F_{107}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{107}$
Dimension:	$2$
L-polynomial:	$( 1 - 18 x + 107 x^{2} )( 1 - 16 x + 107 x^{2} )$
	$1 - 34 x + 502 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.164078095836$, $\pm0.218559897265$
Angle rank:	$2$ (numerical)
Jacobians:	$36$
Isomorphism classes:	96

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8280$	$129366720$	$1501940639160$	$17186047922534400$	$196721124782456201400$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11298$	$1226030$	$131111534$	$14025944314$	$1500734167506$	$160578167903038$	$17181861759394846$	$1838459209921183850$	$196715135693534506818$

Jacobians and polarizations

This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=57x^6+27x^5+5x^4+19x^3+5x^2+27x+57$
• $y^2=34x^6+73x^5+91x^4+6x^3+91x^2+73x+34$
• $y^2=77x^6+97x^5+99x^4+74x^3+99x^2+97x+77$
• $y^2=53x^6+67x^5+51x^4+18x^3+88x^2+65x+57$
• $y^2=65x^6+105x^5+77x^4+69x^3+93x^2+30x+80$
• $y^2=45x^6+65x^5+63x^4+38x^3+94x^2+82x+80$
• $y^2=32x^6+51x^5+2x^4+62x^3+2x^2+51x+32$
• $y^2=15x^6+37x^5+78x^4+54x^3+78x^2+37x+15$
• $y^2=93x^6+48x^5+55x^4+99x^3+15x^2+92x+17$
• $y^2=6x^6+2x^5+59x^4+81x^3+73x^2+95x+28$
• $y^2=80x^6+4x^5+99x^4+64x^3+89x^2+47x+82$
• $y^2=50x^6+99x^4+43x^3+99x^2+50$
• $y^2=20x^6+10x^5+36x^4+93x^3+9x^2+14x+7$
• $y^2=64x^6+92x^5+102x^4+23x^3+89x^2+41x+85$
• $y^2=29x^6+42x^5+79x^4+27x^3+79x^2+42x+29$
• $y^2=60x^6+39x^5+62x^4+67x^3+62x^2+39x+60$
• $y^2=42x^6+92x^5+64x^4+50x^3+64x^2+92x+42$
• $y^2=39x^6+42x^5+63x^4+104x^3+63x^2+42x+39$
• $y^2=82x^6+31x^5+77x^4+56x^3+58x^2+55x+80$
• $y^2=91x^6+34x^5+30x^4+59x^3+30x^2+34x+91$
• and

• $y^2=15x^6+82x^5+16x^4+85x^3+16x^2+82x+15$
• $y^2=105x^6+27x^5+31x^4+21x^3+31x^2+27x+105$
• $y^2=18x^6+38x^5+82x^4+36x^3+31x^2+80x+51$
• $y^2=60x^6+20x^5+96x^4+3x^3+96x^2+20x+60$
• $y^2=6x^6+8x^5+11x^4+46x^3+11x^2+8x+6$
• $y^2=76x^6+92x^5+35x^4+92x^3+89x^2+86x+48$
• $y^2=2x^6+18x^5+84x^4+101x^3+84x^2+18x+2$
• $y^2=91x^6+15x^5+57x^4+60x^3+57x^2+15x+91$
• $y^2=17x^6+91x^5+56x^4+105x^3+44x^2+60x+55$
• $y^2=72x^6+50x^5+2x^4+91x^3+2x^2+50x+72$
• $y^2=26x^6+13x^5+103x^4+75x^3+98x^2+19x+32$
• $y^2=73x^6+72x^5+99x^4+82x^3+30x^2+103x+91$
• $y^2=82x^6+81x^5+25x^4+18x^3+52x^2+101x+95$
• $y^2=x^6+8x^5+97x^4+76x^3+45x^2+55x+56$
• $y^2=59x^6+23x^5+99x^4+38x^3+53x^2+105x+84$
• $y^2=88x^6+57x^5+82x^4+6x^3+106x^2+47x+65$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{107}$

The isogeny class factors as 1.107.as $\times$ 1.107.aq and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.107.as : \(\Q(\sqrt{-26}) \).
• 1.107.aq : \(\Q(\sqrt{-43}) \).

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.ac_acw	$2$	(not in LMFDB)
2.107.c_acw	$2$	(not in LMFDB)
2.107.bi_ti	$2$	(not in LMFDB)