Properties

 Label 2.113.abn_xh Base Field $\F_{113}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{113}$ Dimension: $2$ L-polynomial: $1 - 39 x + 605 x^{2} - 4407 x^{3} + 12769 x^{4}$ Frobenius angles: $\pm0.0784394555333$, $\pm0.167562406750$ Angle rank: $2$ (numerical) Number field: 4.0.76725.1 Galois group: $D_{4}$ Jacobians: 4

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

• $y^2=95x^6+58x^5+98x^4+6x^3+105x^2+35x+17$
• $y^2=8x^6+10x^5+40x^4+38x^3+74x^2+64x+12$
• $y^2=83x^6+94x^5+32x^4+98x^3+80x^2+47x+93$
• $y^2=14x^6+50x^5+32x^4+110x^3+7x^2+111x+101$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8929 159123709 2079422316409 26584264839081141 339459443628842308864 4334528553978043026275101 55347532752408115210035321169 706732560224911260203707837953189 9024267971181897152754045932532582841 115230877650424305847101883920807305089024

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 75 12459 1441143 163046275 18424498590 2081954372163 235260579014991 26584442212881379 3004041939986110779 339456739001621333214

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The endomorphism algebra of this simple isogeny class is 4.0.76725.1.
All geometric endomorphisms are defined over $\F_{113}$.

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.bn_xh $2$ (not in LMFDB)