Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 25 x + 311 x^{2} - 2825 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0552381004409$, $\pm0.438852685630$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.476709525.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $24$ |
| Isomorphism classes: | 48 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $10231$ | $162990061$ | $2080833664039$ | $26578248283257541$ | $339449406176107357936$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $89$ | $12767$ | $1442123$ | $163009371$ | $18423953794$ | $2081951466743$ | $235260567247543$ | $26584441858794163$ | $3004041934529954549$ | $339456738985616425022$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):
- $y^2=76 x^6+26 x^5+83 x^4+110 x^3+108 x^2+21 x+19$
- $y^2=78 x^6+106 x^5+25 x^4+37 x^3+101 x^2+79 x+87$
- $y^2=7 x^6+20 x^5+56 x^4+82 x^3+85 x^2+111 x+112$
- $y^2=8 x^6+30 x^5+71 x^4+9 x^3+45 x^2+30 x+44$
- $y^2=71 x^6+68 x^5+96 x^4+63 x^3+79 x^2+112 x+59$
- $y^2=39 x^6+3 x^5+105 x^4+79 x^3+76 x^2+70 x+59$
- $y^2=98 x^6+70 x^5+79 x^4+109 x^3+15 x^2+46 x+53$
- $y^2=21 x^6+107 x^5+23 x^4+11 x^3+54 x^2+29 x+21$
- $y^2=107 x^6+48 x^5+93 x^4+68 x^3+9 x^2+107 x+58$
- $y^2=39 x^6+21 x^5+49 x^4+14 x^3+79 x^2+104 x+38$
- $y^2=62 x^6+43 x^5+65 x^4+14 x^3+27 x^2+78 x$
- $y^2=107 x^6+61 x^5+72 x^4+92 x^3+27 x^2+53 x+10$
- $y^2=47 x^6+96 x^5+17 x^4+107 x^3+17 x^2+47 x+71$
- $y^2=93 x^6+74 x^5+89 x^4+93 x^3+92 x^2+5 x+30$
- $y^2=24 x^6+7 x^5+67 x^4+103 x^3+95 x^2+17 x+44$
- $y^2=85 x^6+96 x^5+8 x^4+81 x^3+67 x^2+67 x+5$
- $y^2=24 x^6+112 x^5+24 x^4+45 x^3+83 x+78$
- $y^2=48 x^6+53 x^5+45 x^4+11 x^3+95 x^2+32 x+66$
- $y^2=65 x^6+x^5+58 x^4+22 x^3+32 x^2+33 x+70$
- $y^2=10 x^6+9 x^5+87 x^4+79 x^3+28 x^2+95 x+107$
- $y^2=51 x^6+26 x^5+57 x^4+49 x^3+16 x^2+36 x+2$
- $y^2=91 x^6+97 x^5+107 x^4+71 x^3+77 x^2+40 x+51$
- $y^2=38 x^6+55 x^5+46 x^4+13 x^3+29 x^2+14 x+27$
- $y^2=47 x^6+89 x^5+69 x^4+54 x^3+46 x^2+37 x+94$
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 4.0.476709525.1. |
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.z_lz | $2$ | (not in LMFDB) |