Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 29 x + 392 x^{2} - 3277 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0321312236985$, $\pm0.379653757769$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.877212.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $30$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9856$ | $162308608$ | $2081782269952$ | $26580369856251904$ | $339447612606075842176$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $85$ | $12713$ | $1442782$ | $163022385$ | $18423856445$ | $2081947526174$ | $235260539286557$ | $26584442027510305$ | $3004041936747520702$ | $339456738943032349913$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 30 curves (of which all are hyperelliptic):
- $y^2=9 x^6+93 x^5+9 x^4+109 x^3+22 x^2+58 x+49$
- $y^2=52 x^6+105 x^5+61 x^4+27 x^3+71 x^2+92 x+53$
- $y^2=112 x^6+94 x^5+41 x^4+59 x^3+17 x^2+17 x+48$
- $y^2=73 x^6+83 x^5+61 x^4+44 x^3+41 x^2+87 x+44$
- $y^2=46 x^6+26 x^5+7 x^4+59 x^3+50 x^2+25 x+17$
- $y^2=65 x^6+64 x^5+76 x^3+39 x^2+99 x+65$
- $y^2=54 x^6+11 x^5+30 x^4+96 x^3+112 x^2+23 x+27$
- $y^2=109 x^6+32 x^5+66 x^4+70 x^3+48 x^2+78 x+87$
- $y^2=32 x^6+71 x^5+57 x^4+80 x^3+50 x^2+107 x+21$
- $y^2=108 x^6+10 x^5+78 x^4+75 x^3+51 x^2+81 x+69$
- $y^2=48 x^6+57 x^5+3 x^4+9 x^3+79 x^2+49 x+15$
- $y^2=8 x^6+19 x^5+111 x^4+102 x^3+45 x^2+7 x+10$
- $y^2=21 x^6+33 x^5+104 x^4+17 x^3+109 x^2+56 x+34$
- $y^2=73 x^6+12 x^5+85 x^4+53 x^3+50 x^2+38 x+67$
- $y^2=58 x^6+50 x^5+30 x^4+99 x^3+99 x^2+108 x+80$
- $y^2=54 x^6+26 x^5+36 x^4+35 x^3+62 x^2+42 x+10$
- $y^2=74 x^6+95 x^5+11 x^4+49 x^3+78 x^2+86 x+19$
- $y^2=27 x^6+56 x^5+3 x^4+111 x^3+68 x^2+98 x+44$
- $y^2=16 x^6+37 x^5+57 x^4+63 x^3+19 x^2+19 x+37$
- $y^2=94 x^6+52 x^5+33 x^4+97 x^3+19 x^2+80 x+80$
- $y^2=31 x^6+77 x^5+69 x^4+80 x^3+110 x^2+97 x+47$
- $y^2=3 x^6+64 x^5+13 x^4+17 x^3+89 x^2+68 x+60$
- $y^2=90 x^6+99 x^5+93 x^4+52 x^3+101 x^2+56 x+26$
- $y^2=30 x^6+107 x^5+108 x^4+48 x^3+20 x^2+80 x+12$
- $y^2=87 x^6+91 x^5+79 x^4+30 x^3+62 x^2+32 x+106$
- $y^2=93 x^6+100 x^5+109 x^4+19 x^3+22 x^2+80 x+42$
- $y^2=48 x^6+71 x^5+38 x^4+34 x^3+107 x^2+62 x+104$
- $y^2=82 x^6+62 x^5+79 x^4+55 x^3+95 x^2+112 x+70$
- $y^2=22 x^6+112 x^5+60 x^4+80 x^3+63 x^2+111 x+15$
- $y^2=104 x^6+74 x^5+32 x^4+55 x^3+72 x^2+19 x+59$
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 4.0.877212.1. |
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.bd_pc | $2$ | (not in LMFDB) |