Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 29 x + 373 x^{2} - 2407 x^{3} + 6889 x^{4}$ |
Frobenius angles: | $\pm0.147367193729$, $\pm0.254584002254$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1911221.1 |
Galois group: | $D_{4}$ |
Jacobians: | $16$ |
Isomorphism classes: | 16 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4827$ | $46817073$ | $327422085741$ | $2253126554551629$ | $15516699636345046032$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $55$ | $6795$ | $572629$ | $47475899$ | $3939207800$ | $326941343415$ | $27136053285935$ | $2252292218161699$ | $186940255189035577$ | $15516041188987333350$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=66x^6+66x^5+71x^4+54x^3+80x^2+25x+14$
- $y^2=76x^6+78x^5+69x^4+71x^3+45x^2+41x+10$
- $y^2=39x^6+59x^5+21x^4+71x^3+29x^2+62x+26$
- $y^2=48x^6+38x^5+72x^4+49x^3+6x^2+64x+17$
- $y^2=58x^6+3x^5+4x^4+35x^3+63x^2+13x+14$
- $y^2=60x^6+66x^5+60x^4+45x^3+80x^2+34x+72$
- $y^2=15x^6+41x^5+8x^4+22x^3+48x^2+16x+36$
- $y^2=47x^6+57x^5+77x^4+53x^3+73x^2+58x+47$
- $y^2=x^6+64x^4+40x^3+61x^2+41x+67$
- $y^2=40x^6+11x^5+49x^4+74x^3+64x^2+67x+42$
- $y^2=80x^6+37x^5+33x^4+x^3+30x^2+23x+6$
- $y^2=32x^6+47x^5+4x^4+26x^3+3x^2+14x+11$
- $y^2=59x^6+27x^5+39x^4+10x^3+24x^2+16x+62$
- $y^2=55x^6+9x^5+40x^4+60x^3+59x^2+76x+45$
- $y^2=14x^6+27x^5+36x^4+20x^3+12x^2+58x+67$
- $y^2=15x^6+60x^5+42x^4+71x^3+31x^2+56x+9$
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 4.0.1911221.1. |
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_oj | $2$ | (not in LMFDB) |