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

• Label: 2.107.abi_tf
• 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:	$( 1 - 19 x + 107 x^{2} )( 1 - 15 x + 107 x^{2} )$
	$1 - 34 x + 499 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.129482033963$, $\pm0.241815531636$
Angle rank:	$2$ (numerical)
Jacobians:	$24$
Isomorphism classes:	40

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8277$	$129295017$	$1501564737456$	$17185016651539689$	$196719250667275990077$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11292$	$1225724$	$131103668$	$14025810694$	$1500732600822$	$160578157480066$	$17181861802184356$	$1838459212468074788$	$196715135738678253132$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=x^6+78x^5+14x^4+24x^3+14x^2+78x+1$
• $y^2=82x^6+78x^5+48x^4+87x^3+92x^2+89x+4$
• $y^2=89x^6+84x^5+86x^4+83x^3+86x^2+84x+89$
• $y^2=79x^6+13x^5+85x^4+56x^3+85x^2+13x+79$
• $y^2=38x^6+83x^5+92x^4+52x^3+89x^2+93x+45$
• $y^2=17x^6+64x^5+94x^4+33x^3+53x^2+48x+56$
• $y^2=60x^6+96x^5+101x^4+106x^3+92x^2+37x+82$
• $y^2=64x^6+91x^5+60x^4+51x^3+98x^2+94x+63$
• $y^2=83x^6+72x^5+98x^4+11x^3+45x^2+52x+81$
• $y^2=61x^6+64x^5+56x^4+53x^3+56x^2+64x+61$
• $y^2=87x^6+69x^5+94x^4+44x^3+94x^2+69x+87$
• $y^2=17x^6+42x^5+3x^4+34x^3+55x^2+81x+63$
• $y^2=30x^6+22x^5+16x^4+44x^3+81x^2+33x+100$
• $y^2=5x^6+18x^5+40x^4+74x^3+40x^2+18x+5$
• $y^2=91x^6+45x^5+96x^4+93x^3+81x^2+17x+46$
• $y^2=9x^6+73x^5+13x^4+50x^3+13x^2+73x+9$
• $y^2=66x^6+99x^5+6x^4+60x^3+38x^2+102x+72$
• $y^2=93x^6+78x^5+10x^4+77x^3+10x^2+78x+93$
• $y^2=46x^6+18x^5+96x^4+7x^3+96x^2+18x+46$
• $y^2=x^6+52x^5+42x^4+20x^3+103x^2+29x+17$
• $y^2=82x^6+67x^5+24x^4+41x^3+24x^2+67x+82$
• $y^2=12x^6+105x^5+104x^4+6x^3+104x^2+105x+12$
• $y^2=79x^6+90x^5+105x^4+39x^3+52x^2+70x+91$
• $y^2=73x^6+101x^5+80x^4+65x^3+80x^2+101x+73$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{107}$

The isogeny class factors as 1.107.at $\times$ 1.107.ap 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.at : \(\Q(\sqrt{-67}) \).
• 1.107.ap : \(\Q(\sqrt{-203}) \).

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.ae_act	$2$	(not in LMFDB)
2.107.e_act	$2$	(not in LMFDB)
2.107.bi_tf	$2$	(not in LMFDB)