Invariants
Base field: | $\F_{113}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 37 x + 567 x^{2} - 4181 x^{3} + 12769 x^{4}$ |
Frobenius angles: | $\pm0.125932323751$, $\pm0.195315764367$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.251525.1 |
Galois group: | $D_{4}$ |
Jacobians: | $11$ |
Isomorphism classes: | 11 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $9119$ | $160084045$ | $2081580351191$ | $26587709893247525$ | $339463708769380319344$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $77$ | $12535$ | $1442639$ | $163067403$ | $18424730082$ | $2081956303855$ | $235260589050179$ | $26584442191425363$ | $3004041938639982977$ | $339456738981053615550$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 11 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=22x^6+41x^5+47x^4+71x^3+19x^2+5x+10$
- $y^2=83x^6+45x^5+12x^4+94x^3+22x^2+20x+2$
- $y^2=108x^6+103x^5+93x^4+63x^3+44x^2+97x+59$
- $y^2=107x^6+22x^5+45x^4+72x^3+86x^2+95x+73$
- $y^2=20x^6+24x^5+2x^4+99x^3+101x+52$
- $y^2=36x^6+62x^5+36x^4+110x^3+12x^2+106x+40$
- $y^2=50x^6+29x^5+107x^4+65x^3+16x+70$
- $y^2=58x^6+31x^5+40x^4+70x^3+88x^2+93x+43$
- $y^2=94x^6+67x^5+101x^4+107x^3+29x^2+102x+41$
- $y^2=110x^6+103x^5+89x^4+105x^3+32x^2+71x+109$
- $y^2=59x^6+89x^5+61x^4+39x^3+89x^2+24x+48$
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 4.0.251525.1. |
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.bl_vv | $2$ | (not in LMFDB) |