Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 32 x + 459 x^{2} - 3616 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0666574284727$, $\pm0.323316868959$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.53974928.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9581$ | $161698537$ | $2082596407892$ | $26584173615248249$ | $339452446315697644501$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $82$ | $12664$ | $1443346$ | $163045716$ | $18424118802$ | $2081948025862$ | $235260524059762$ | $26584442050638564$ | $3004041942382938802$ | $339456739038034077384$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 28 curves (of which all are hyperelliptic):
- $y^2=76 x^6+83 x^5+50 x^4+93 x^3+15 x^2+12 x+84$
- $y^2=105 x^6+21 x^5+111 x^4+35 x^3+99 x^2+74 x+52$
- $y^2=102 x^6+70 x^5+27 x^4+76 x^3+45 x^2+67 x+86$
- $y^2=10 x^6+74 x^5+112 x^4+40 x^3+75 x^2+65 x+34$
- $y^2=68 x^6+69 x^5+82 x^4+91 x^3+106 x^2+66 x+99$
- $y^2=70 x^6+76 x^5+48 x^4+107 x^3+109 x^2+27 x+25$
- $y^2=80 x^6+78 x^5+66 x^4+94 x^3+31 x^2+89 x+51$
- $y^2=21 x^6+91 x^5+40 x^4+63 x^3+107 x^2+88 x+40$
- $y^2=111 x^6+29 x^5+35 x^4+70 x^3+105 x^2+89 x+47$
- $y^2=62 x^6+72 x^5+94 x^4+16 x^3+64 x^2+62 x+48$
- $y^2=5 x^6+44 x^5+30 x^4+2 x^3+47 x^2+42 x+94$
- $y^2=22 x^6+60 x^5+49 x^4+66 x^3+81 x^2+19 x+17$
- $y^2=4 x^6+88 x^5+74 x^4+71 x^3+24 x^2+97 x+27$
- $y^2=41 x^6+17 x^5+23 x^4+2 x^3+86 x^2+98 x+7$
- $y^2=46 x^6+95 x^5+31 x^4+30 x^3+112 x^2+94 x+105$
- $y^2=2 x^6+61 x^5+69 x^4+11 x^3+105 x^2+55 x+79$
- $y^2=103 x^6+94 x^5+80 x^4+101 x^3+64 x^2+26 x+66$
- $y^2=45 x^6+59 x^5+111 x^4+21 x^3+105 x^2+24 x+34$
- $y^2=71 x^6+89 x^5+100 x^4+x^3+x^2+17 x+8$
- $y^2=3 x^6+34 x^5+107 x^4+31 x^3+55 x^2+26 x+13$
- $y^2=41 x^6+45 x^5+21 x^4+15 x^3+3 x^2+39 x+65$
- $y^2=x^6+50 x^5+76 x^4+64 x^3+17 x^2+34 x+75$
- $y^2=75 x^6+101 x^5+33 x^4+65 x^3+69 x^2+67 x+54$
- $y^2=33 x^6+79 x^5+5 x^4+76 x^3+23 x^2+11 x+104$
- $y^2=55 x^6+20 x^5+99 x^4+40 x^3+19 x^2+4 x+107$
- $y^2=53 x^6+46 x^5+94 x^4+22 x^3+98 x^2+78 x+54$
- $y^2=77 x^6+98 x^5+104 x^4+8 x^3+53 x^2+84 x+64$
- $y^2=64 x^6+80 x^5+82 x^4+93 x^3+51 x^2+97 x+111$
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 4.0.53974928.1. |
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.bg_rr | $2$ | (not in LMFDB) |