Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 34 x + 498 x^{2} - 3842 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0361800547850$, $\pm0.292901901285$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.120224.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $28$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9392$ | $161016448$ | $2081900530736$ | $26584274139643904$ | $339453080056439805232$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $80$ | $12610$ | $1442864$ | $163046334$ | $18424153200$ | $2081947424770$ | $235260496282640$ | $26584441574542974$ | $3004041937616392592$ | $339456739012658074050$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 28 curves (of which all are hyperelliptic):
- $y^2=41 x^6+72 x^5+45 x^4+54 x^3+48 x^2+104 x+45$
- $y^2=6 x^6+91 x^5+62 x^4+92 x^3+97 x^2+75 x+66$
- $y^2=40 x^6+85 x^5+57 x^4+20 x^3+71 x^2+103 x+45$
- $y^2=85 x^6+106 x^5+81 x^4+47 x^3+37 x^2+9 x+111$
- $y^2=32 x^6+35 x^5+5 x^4+40 x^3+11 x^2+106 x+96$
- $y^2=90 x^6+65 x^5+98 x^4+83 x^3+81 x^2+43 x+102$
- $y^2=11 x^6+112 x^5+16 x^4+94 x^3+67 x^2+73 x+91$
- $y^2=39 x^6+86 x^5+112 x^4+71 x^3+3 x^2+19 x+38$
- $y^2=74 x^6+61 x^5+94 x^4+5 x^3+67 x^2+83 x+44$
- $y^2=5 x^6+93 x^5+88 x^4+71 x^3+79 x^2+109 x+112$
- $y^2=22 x^6+42 x^5+75 x^4+110 x^3+9 x^2+105 x+43$
- $y^2=63 x^6+91 x^5+60 x^4+9 x^3+36 x^2+x+34$
- $y^2=39 x^6+93 x^5+92 x^4+20 x^3+22 x^2+93 x+80$
- $y^2=75 x^6+90 x^5+98 x^4+27 x^3+106 x^2+74 x+105$
- $y^2=16 x^6+79 x^5+74 x^4+48 x^3+84 x^2+29 x+103$
- $y^2=40 x^6+106 x^5+72 x^4+77 x^3+97 x^2+61 x+53$
- $y^2=39 x^6+81 x^5+10 x^4+37 x^3+35 x^2+33 x+22$
- $y^2=79 x^6+104 x^5+105 x^4+106 x^3+109 x^2+91 x+59$
- $y^2=10 x^6+77 x^5+103 x^4+106 x^3+96 x^2+94 x+81$
- $y^2=12 x^6+25 x^5+52 x^4+49 x^3+94 x^2+45 x+74$
- $y^2=14 x^6+37 x^5+29 x^4+37 x^3+98 x^2+6 x+12$
- $y^2=55 x^6+2 x^5+45 x^4+71 x^3+46 x^2+75 x+55$
- $y^2=94 x^6+50 x^5+72 x^4+44 x^3+47 x^2+40 x+36$
- $y^2=80 x^6+66 x^5+60 x^4+34 x^3+78 x^2+41 x+75$
- $y^2=89 x^6+93 x^5+13 x^4+33 x^3+80 x^2+106 x+99$
- $y^2=103 x^6+2 x^5+67 x^4+6 x^3+106 x^2+x+72$
- $y^2=5 x^6+68 x^5+12 x^4+23 x^3+8 x^2+101 x+47$
- $y^2=90 x^6+82 x^5+49 x^4+69 x^3+67 x^2+27 x+80$
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 4.0.120224.1. |
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 |
|---|---|---|
| 2.113.bi_te | $2$ | (not in LMFDB) |