Invariants
Base field: | $\F_{113}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 113 x^{2} )( 1 - 18 x + 113 x^{2} )$ |
$1 - 39 x + 604 x^{2} - 4407 x^{3} + 12769 x^{4}$ | |
Frobenius angles: | $\pm0.0498602789898$, $\pm0.178616545187$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $7$ |
Isomorphism classes: | 35 |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8928$ | $159096960$ | $2079252955008$ | $26583666961420800$ | $339457916682754407648$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $75$ | $12457$ | $1441026$ | $163042609$ | $18424415715$ | $2081952863134$ | $235260555704067$ | $26584441899409441$ | $3004041936279413538$ | $339456738963218557657$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 7 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=84x^6+27x^5+31x^4+60x^3+105x^2+111x+17$
- $y^2=83x^6+18x^5+112x^4+29x^3+61x^2+42x+80$
- $y^2=70x^6+24x^5+23x^4+54x^3+76x^2+21x+54$
- $y^2=12x^6+109x^5+95x^4+72x^3+90x^2+3x+96$
- $y^2=83x^6+40x^5+92x^4+26x^3+78x^2+59x$
- $y^2=76x^6+42x^5+33x^4+107x^3+71x^2+32x+25$
- $y^2=58x^6+92x^5+58x^4+3x^3+81x^2+64x+85$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$The isogeny class factors as 1.113.av $\times$ 1.113.as and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ad_afw | $2$ | (not in LMFDB) |
2.113.d_afw | $2$ | (not in LMFDB) |
2.113.bn_xg | $2$ | (not in LMFDB) |