Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 23 x + 266 x^{2} - 2599 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0385352257771$, $\pm0.471585571022$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.4969036.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $24$ |
| Isomorphism classes: | 24 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $10414$ | $163062412$ | $2079630145024$ | $26576856365250304$ | $339450466982120291374$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $91$ | $12773$ | $1441288$ | $163000833$ | $18424011371$ | $2081952076898$ | $235260545685179$ | $26584441497901441$ | $3004041933884871784$ | $339456739002351986693$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=28 x^6+31 x^5+87 x^4+24 x^3+x^2+34 x+69$
- $y^2=10 x^6+3 x^5+100 x^4+26 x^3+21 x^2+6 x+96$
- $y^2=45 x^6+54 x^5+20 x^4+56 x^3+79 x^2+63 x+57$
- $y^2=87 x^6+77 x^5+102 x^4+84 x^3+31 x^2+100 x+90$
- $y^2=49 x^6+85 x^5+79 x^4+6 x^3+110 x^2+82 x+103$
- $y^2=97 x^6+100 x^5+57 x^4+93 x^3+29 x^2+106 x+46$
- $y^2=78 x^6+108 x^5+61 x^4+81 x^3+69 x^2+105 x+67$
- $y^2=103 x^6+109 x^5+28 x^4+72 x^3+53 x^2+30 x+32$
- $y^2=107 x^6+22 x^5+105 x^4+33 x^3+67 x^2+2 x+47$
- $y^2=42 x^6+38 x^5+35 x^4+49 x^3+60 x^2+50 x+58$
- $y^2=54 x^6+34 x^5+102 x^4+68 x^3+90 x^2+46 x+48$
- $y^2=41 x^6+77 x^5+13 x^4+101 x^3+7 x^2+69 x+35$
- $y^2=50 x^6+16 x^5+60 x^4+27 x^3+59 x^2+90 x+105$
- $y^2=6 x^6+14 x^5+87 x^4+35 x^3+101 x^2+30 x+110$
- $y^2=73 x^6+99 x^5+76 x^4+38 x^3+19 x^2+30 x+112$
- $y^2=42 x^6+73 x^5+60 x^4+68 x^3+68 x^2+45 x+58$
- $y^2=47 x^6+48 x^5+91 x^4+7 x^3+104 x^2+80 x+107$
- $y^2=82 x^6+110 x^5+10 x^4+15 x^3+5 x^2+17 x+12$
- $y^2=30 x^6+71 x^5+88 x^4+61 x^3+101 x^2+64 x+57$
- $y^2=55 x^6+86 x^5+49 x^4+23 x^3+9 x^2+30 x+18$
- $y^2=21 x^6+42 x^5+12 x^4+83 x^3+42 x^2+30 x+38$
- $y^2=18 x^6+22 x^5+53 x^4+55 x^3+101 x^2+65 x+84$
- $y^2=8 x^6+111 x^5+6 x^4+102 x^3+22 x^2+21 x+2$
- $y^2=33 x^6+112 x^5+80 x^4+106 x^3+19 x^2+11 x+34$
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 4.0.4969036.1. |
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.x_kg | $2$ | (not in LMFDB) |