Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 29 x + 395 x^{2} - 3277 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0568076324561$, $\pm0.375948702935$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.149982525.2 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9859$ | $162387589$ | $2082159289699$ | $26581245391408981$ | $339448951024860898864$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $85$ | $12719$ | $1443043$ | $163027755$ | $18423929090$ | $2081948365343$ | $235260550678511$ | $26584442208572659$ | $3004041939347134729$ | $339456738973222273214$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 28 curves (of which all are hyperelliptic):
- $y^2=84 x^6+40 x^5+102 x^4+10 x^3+65 x^2+79 x+40$
- $y^2=39 x^6+101 x^5+41 x^4+15 x^3+35 x^2+49 x+10$
- $y^2=112 x^6+69 x^5+60 x^4+27 x^3+73 x^2+104 x+45$
- $y^2=85 x^6+87 x^5+108 x^4+22 x^3+17 x^2+20 x+112$
- $y^2=103 x^6+23 x^5+57 x^4+6 x^3+110 x^2+3 x+14$
- $y^2=96 x^6+83 x^5+59 x^4+106 x^3+32 x^2+65 x+84$
- $y^2=88 x^6+26 x^5+23 x^4+69 x^3+67 x^2+103 x+40$
- $y^2=85 x^6+8 x^5+25 x^4+81 x^3+6 x^2+43 x+103$
- $y^2=38 x^6+31 x^5+60 x^4+43 x^3+8 x^2+97 x+28$
- $y^2=51 x^6+71 x^5+85 x^4+97 x^3+21 x^2+91 x+98$
- $y^2=63 x^6+26 x^5+41 x^4+55 x^3+111 x^2+80 x+52$
- $y^2=90 x^5+109 x^4+101 x^3+82 x^2+4 x+107$
- $y^2=79 x^6+108 x^5+112 x^4+84 x^3+51 x^2+11 x+92$
- $y^2=32 x^6+6 x^5+10 x^4+94 x^3+51 x^2+77 x+96$
- $y^2=87 x^6+81 x^5+112 x^4+106 x^3+38 x^2+49 x+58$
- $y^2=15 x^6+34 x^5+57 x^4+97 x^3+105 x^2+40 x+36$
- $y^2=57 x^6+71 x^5+103 x^4+x^3+64 x^2+62 x+29$
- $y^2=66 x^6+108 x^5+42 x^4+21 x^3+12 x^2+92 x+17$
- $y^2=38 x^6+98 x^5+110 x^4+68 x^3+108 x^2+23 x+105$
- $y^2=35 x^6+9 x^5+85 x^4+97 x^3+88 x^2+103 x+93$
- $y^2=12 x^6+22 x^5+71 x^4+44 x^3+x^2+88 x+108$
- $y^2=54 x^6+48 x^5+16 x^4+16 x^3+69 x^2+61 x+92$
- $y^2=68 x^6+73 x^5+6 x^4+36 x^3+85 x^2+15$
- $y^2=22 x^6+46 x^5+25 x^4+100 x^3+75 x^2+83 x+33$
- $y^2=32 x^6+55 x^5+12 x^4+107 x^3+60 x^2+31 x+103$
- $y^2=33 x^6+87 x^5+87 x^4+95 x^3+86 x^2+37 x+62$
- $y^2=38 x^6+68 x^5+47 x^4+92 x^3+31 x^2+104 x+55$
- $y^2=107 x^6+32 x^5+76 x^4+84 x^3+101 x^2+40 x+10$
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 4.0.149982525.2. |
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.bd_pf | $2$ | (not in LMFDB) |