Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 29 x + 375 x^{2} - 2407 x^{3} + 6889 x^{4}$ |
Frobenius angles: | $\pm0.172232313838$, $\pm0.237449215783$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.336725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $7$ |
Isomorphism classes: | 7 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4829$ | $46846129$ | $327521955959$ | $2253303911128061$ | $15516900689876826064$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $55$ | $6799$ | $572803$ | $47479635$ | $3939258840$ | $326941778683$ | $27136054228261$ | $2252292177439539$ | $186940254346203589$ | $15516041179113587814$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 7 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=60x^6+43x^5+51x^4+26x^3+47x^2+67x+26$
- $y^2=63x^6+7x^5+78x^4+10x^3+37x^2+69x+65$
- $y^2=75x^6+9x^5+39x^4+78x^3+42x^2+78x$
- $y^2=13x^6+35x^5+58x^4+54x^3+55x^2+6x+57$
- $y^2=38x^6+73x^5+79x^4+65x^3+70x^2+19x+43$
- $y^2=82x^6+40x^5+78x^4+2x^3+53x^2+62x+23$
- $y^2=42x^6+61x^5+77x^4+48x^3+34x^2+41x+76$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$The endomorphism algebra of this simple isogeny class is 4.0.336725.1. |
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 |
---|---|---|
2.83.bd_ol | $2$ | (not in LMFDB) |