Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 35 x + 529 x^{2} - 3955 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.137664879391$, $\pm0.235612203595$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2758925.3 |
| Galois group: | $D_{4}$ |
| Jacobians: | $18$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9309$ | $160943301$ | $2083115228661$ | $26589198285335781$ | $339463767954118059264$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $79$ | $12603$ | $1443703$ | $163076531$ | $18424733294$ | $2081954990907$ | $235260564656063$ | $26584441933772323$ | $3004041937297790839$ | $339456738990052731678$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which all are hyperelliptic):
- $y^2=68 x^6+4 x^5+5 x^4+64 x^3+50 x^2+111 x+14$
- $y^2=63 x^6+33 x^5+29 x^4+97 x^3+41 x^2+12 x+67$
- $y^2=110 x^6+100 x^5+95 x^4+56 x^3+30 x^2+109 x+102$
- $y^2=42 x^6+42 x^5+104 x^4+5 x^3+32 x^2+15 x+78$
- $y^2=95 x^6+9 x^5+52 x^4+40 x^3+72 x^2+11 x+7$
- $y^2=58 x^6+51 x^5+101 x^4+42 x^3+36 x^2+67 x+55$
- $y^2=6 x^6+100 x^5+73 x^4+74 x^3+15 x^2+98 x+110$
- $y^2=39 x^6+47 x^5+68 x^4+73 x^3+29 x^2+88 x+53$
- $y^2=10 x^6+24 x^5+86 x^4+57 x^3+90 x^2+84 x+42$
- $y^2=14 x^6+93 x^5+111 x^4+10 x^3+87 x^2+37 x+18$
- $y^2=17 x^6+8 x^5+52 x^4+51 x^3+86 x^2+44 x+105$
- $y^2=103 x^6+6 x^5+5 x^4+73 x^3+83 x^2+25 x+47$
- $y^2=60 x^6+87 x^5+39 x^4+68 x^3+33 x^2+61 x+38$
- $y^2=39 x^6+60 x^5+90 x^4+26 x^3+67 x^2+94 x+111$
- $y^2=53 x^6+84 x^5+33 x^4+70 x^3+84 x^2+33 x+55$
- $y^2=75 x^6+63 x^5+71 x^4+43 x^3+59 x^2+57 x+103$
- $y^2=58 x^6+99 x^5+40 x^4+89 x^3+24 x^2+108 x+63$
- $y^2=24 x^6+32 x^5+53 x^4+74 x^3+64 x^2+44 x+25$
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 4.0.2758925.3. |
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.bj_uj | $2$ | (not in LMFDB) |