Invariants
Base field: | $\F_{113}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 37 x + 564 x^{2} - 4181 x^{3} + 12769 x^{4}$ |
Frobenius angles: | $\pm0.0818341620435$, $\pm0.218655119859$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.95948.1 |
Galois group: | $D_{4}$ |
Jacobians: | $14$ |
Isomorphism classes: | 14 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $9116$ | $160004032$ | $2081098495232$ | $26586137473781504$ | $339460119564550357276$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $77$ | $12529$ | $1442306$ | $163057761$ | $18424535277$ | $2081953278622$ | $235260552060317$ | $26584441851324609$ | $3004041936880519202$ | $339456738992531951409$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=80x^6+11x^5+98x^4+49x^3+96x^2+98x+7$
- $y^2=15x^6+19x^5+12x^4+42x^3+93x^2+44x+56$
- $y^2=78x^6+20x^5+63x^4+22x^3+107x^2+50x+76$
- $y^2=15x^6+3x^5+68x^4+16x^3+96x^2+66x+42$
- $y^2=28x^6+49x^5+61x^4+33x^3+68x^2+52x+71$
- $y^2=73x^6+65x^5+93x^4+18x^3+106x^2+55x+83$
- $y^2=67x^6+12x^5+65x^4+28x^3+66x^2+79x+10$
- $y^2=78x^6+48x^5+81x^4+61x^3+23x^2+59x+101$
- $y^2=79x^6+101x^5+49x^4+24x^3+32x^2+98x+6$
- $y^2=31x^6+46x^5+83x^4+38x^3+82x^2+23x+63$
- $y^2=74x^6+31x^5+98x^4+71x^3+33x^2+19x+43$
- $y^2=86x^6+17x^5+5x^4+x^3+23x^2+95x+31$
- $y^2=3x^6+43x^5+29x^4+24x^3+61x^2+12x+54$
- $y^2=90x^6+4x^5+87x^4+83x^3+70x^2+35x+112$
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 4.0.95948.1. |
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_vs | $2$ | (not in LMFDB) |