Abelian variety isogeny class 2.113.abi_tp over $\F_{113}$

• Label: 2.113.abi_tp
• Base field: $\F_{113}$
• 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:	$\F_{113}$
Dimension:	$2$
L-polynomial:	$1 - 34 x + 509 x^{2} - 3842 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.132326794770$, $\pm0.260064913325$
Angle rank:	$2$ (numerical)
Number field:	4.0.10202688.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9403$	$161308465$	$2083523096428$	$26588955791718025$	$339462106911302530723$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$80$	$12632$	$1443986$	$163075044$	$18424643140$	$2081953510454$	$235260551977972$	$26584441933928836$	$3004041939181125938$	$339456739023104705432$

Jacobians and polarizations

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

• $y^2=40 x^6+76 x^5+7 x^4+38 x^3+71 x^2+6 x+6$
• $y^2=98 x^6+94 x^5+93 x^4+49 x^3+11 x^2+26 x+61$
• $y^2=57 x^6+37 x^5+107 x^4+35 x^3+59 x^2+8 x+38$
• $y^2=47 x^6+104 x^5+39 x^4+109 x^3+50 x^2+50 x+44$
• $y^2=22 x^6+93 x^5+105 x^4+15 x^3+108 x^2+52 x+86$
• $y^2=62 x^6+70 x^5+45 x^4+54 x^3+49 x^2+87 x+108$
• $y^2=90 x^6+22 x^5+111 x^4+66 x^3+23 x^2+4 x+5$
• $y^2=79 x^6+13 x^5+36 x^4+25 x^3+19 x^2+73 x+14$
• $y^2=96 x^6+107 x^5+34 x^4+69 x^3+76 x^2+10 x+2$
• $y^2=75 x^6+67 x^5+57 x^4+105 x^3+101 x^2+8 x+42$
• $y^2=20 x^6+24 x^5+7 x^4+78 x^3+61 x^2+63 x+102$
• $y^2=98 x^6+103 x^5+72 x^4+112 x^3+29 x^2+92 x+83$
• $y^2=12 x^6+83 x^5+62 x^4+106 x^3+57 x^2+88 x+43$
• $y^2=98 x^6+60 x^5+39 x^4+92 x^3+5 x^2+22 x+35$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{113}$.

Endomorphism algebra over $\F_{113}$

The endomorphism algebra of this simple isogeny class is 4.0.10202688.2.

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
2.113.bi_tp	$2$	(not in LMFDB)