Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 24 x + 285 x^{2} - 2712 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0197105444322$, $\pm0.458251322724$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.5556025.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $20$ |
| Isomorphism classes: | 40 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $10319$ | $162947329$ | $2079874690544$ | $26576802076930201$ | $339448925230580404439$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $90$ | $12764$ | $1441458$ | $163000500$ | $18423927690$ | $2081951101118$ | $235260544576266$ | $26584441479705124$ | $3004041931836722514$ | $339456738971660776364$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which all are hyperelliptic):
- $y^2=99 x^6+38 x^5+65 x^4+95 x^3+12 x^2+77 x+75$
- $y^2=37 x^6+2 x^5+104 x^4+76 x^3+109 x^2+82 x+102$
- $y^2=108 x^6+27 x^5+110 x^4+14 x^3+100 x^2+23 x+4$
- $y^2=20 x^6+56 x^5+107 x^4+79 x^3+23 x^2+62 x+10$
- $y^2=49 x^6+5 x^5+67 x^4+35 x^3+71 x^2+107 x+107$
- $y^2=46 x^6+28 x^5+65 x^4+65 x^3+14 x^2+82 x+10$
- $y^2=80 x^6+109 x^5+94 x^4+50 x^3+81 x^2+53 x+58$
- $y^2=62 x^6+42 x^5+101 x^4+68 x^3+49 x^2+8 x+74$
- $y^2=61 x^6+107 x^5+14 x^4+27 x^3+12 x^2+22 x+54$
- $y^2=61 x^6+13 x^5+84 x^4+19 x^3+43 x^2+103 x+107$
- $y^2=97 x^6+40 x^5+70 x^4+99 x^3+36 x^2+40 x+98$
- $y^2=90 x^6+36 x^5+83 x^4+55 x^3+35 x^2+61 x+59$
- $y^2=88 x^6+42 x^5+x^4+69 x^3+90 x^2+44 x+25$
- $y^2=10 x^6+89 x^5+52 x^4+72 x^3+72 x^2+86 x+99$
- $y^2=90 x^6+97 x^5+51 x^4+22 x^3+8 x^2+42 x+23$
- $y^2=31 x^6+79 x^5+93 x^4+55 x^3+7 x^2+55 x+43$
- $y^2=43 x^6+80 x^5+80 x^4+6 x^3+96 x^2+106 x+58$
- $y^2=29 x^6+53 x^5+53 x^4+108 x^3+96 x^2+81 x+107$
- $y^2=41 x^6+10 x^5+109 x^4+32 x^3+48 x^2+43 x+112$
- $y^2=44 x^6+40 x^5+77 x^4+54 x^3+108 x^2+20 x+63$
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 4.0.5556025.1. |
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.y_kz | $2$ | (not in LMFDB) |