Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 22 x + 344 x^{2} - 2486 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.295618480499$, $\pm0.356420349651$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.90432.3 |
| Galois group: | $D_{4}$ |
| Jacobians: | $30$ |
| Isomorphism classes: | 30 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $10606$ | $165686932$ | $2088594366622$ | $26588904009943504$ | $339453208145518150126$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $92$ | $12974$ | $1447496$ | $163074726$ | $18424160152$ | $2081946949022$ | $235260517605772$ | $26584442086006654$ | $3004041942413388332$ | $339456739021340340734$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 30 curves (of which all are hyperelliptic):
- $y^2=92 x^6+51 x^5+13 x^4+16 x^3+55 x^2+51 x+78$
- $y^2=11 x^6+16 x^5+111 x^4+78 x^3+7 x^2+48 x+4$
- $y^2=35 x^6+32 x^5+36 x^4+61 x^3+52 x^2+58 x+29$
- $y^2=91 x^6+50 x^5+34 x^4+86 x^3+30 x^2+36 x+50$
- $y^2=49 x^6+33 x^5+11 x^4+4 x^3+67 x+11$
- $y^2=12 x^6+24 x^5+38 x^4+15 x^3+52 x^2+49 x+99$
- $y^2=112 x^6+108 x^5+14 x^4+93 x^3+67 x^2+31 x+76$
- $y^2=49 x^6+12 x^5+37 x^4+18 x^3+44 x^2+70 x+23$
- $y^2=39 x^6+91 x^5+54 x^4+94 x^3+10 x^2+35 x+77$
- $y^2=19 x^6+26 x^5+55 x^4+51 x^3+90 x^2+53 x+18$
- $y^2=104 x^6+3 x^5+67 x^4+94 x^3+77 x^2+23 x+74$
- $y^2=67 x^6+34 x^5+27 x^4+58 x^3+53 x^2+39 x+41$
- $y^2=97 x^6+22 x^5+4 x^4+14 x^3+56 x^2+21 x+3$
- $y^2=59 x^6+6 x^5+103 x^4+3 x^3+95 x^2+111 x+23$
- $y^2=112 x^6+98 x^5+32 x^4+20 x^3+29 x+24$
- $y^2=28 x^6+95 x^5+96 x^4+110 x^3+61 x^2+42 x+110$
- $y^2=106 x^6+41 x^5+39 x^4+98 x^3+16 x^2+38 x+79$
- $y^2=38 x^6+81 x^5+63 x^4+20 x^3+104 x^2+54 x+5$
- $y^2=102 x^6+92 x^5+80 x^4+35 x^3+49 x^2+83 x+21$
- $y^2=100 x^6+47 x^5+41 x^4+2 x^3+19 x^2+31 x+100$
- $y^2=58 x^6+107 x^5+76 x^4+28 x^3+54 x^2+51 x+100$
- $y^2=83 x^6+85 x^5+86 x^4+29 x^3+4 x^2+63 x+16$
- $y^2=84 x^6+97 x^5+43 x^4+63 x^3+3 x^2+20 x+84$
- $y^2=68 x^6+104 x^5+110 x^4+62 x^3+16 x^2+71 x+1$
- $y^2=55 x^6+106 x^5+41 x^4+77 x^3+84 x^2+14 x+36$
- $y^2=108 x^6+99 x^5+13 x^4+93 x^3+30 x^2+97 x+82$
- $y^2=x^6+74 x^5+21 x^4+89 x^3+34 x^2+41 x+54$
- $y^2=86 x^6+44 x^5+x^4+27 x^3+56 x^2+51 x+37$
- $y^2=96 x^6+83 x^5+85 x^4+x^3+61 x^2+32 x+89$
- $y^2=12 x^6+50 x^5+100 x^4+77 x^3+23 x^2+19 x+102$
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 4.0.90432.3. |
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.w_ng | $2$ | (not in LMFDB) |