Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 29 x + 365 x^{2} - 2407 x^{3} + 6889 x^{4}$ |
Frobenius angles: | $\pm0.0639743454557$, $\pm0.290481692689$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.68725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $15$ |
Isomorphism classes: | 15 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4819$ | $46700929$ | $327022693909$ | $2252409576442861$ | $15515849740694096464$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $55$ | $6779$ | $571933$ | $47460795$ | $3938992040$ | $326939174903$ | $27136038928151$ | $2252292185770339$ | $186940255775410009$ | $15516041198082912614$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 15 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=80x^6+25x^5+68x^4+65x^3+9x^2+13x+51$
- $y^2=15x^6+82x^5+31x^4+59x^3+45x^2+7x+81$
- $y^2=79x^6+43x^5+35x^4+29x^3+28x^2+60x+46$
- $y^2=32x^6+25x^5+42x^4+26x^3+54x^2+44x+74$
- $y^2=64x^6+28x^5+16x^4+63x^3+62x^2+53x+10$
- $y^2=64x^6+56x^5+46x^4+x^3+19x^2+12x+70$
- $y^2=x^6+78x^5+46x^4+36x^2+11x+48$
- $y^2=71x^6+20x^5+71x^4+41x^3+49x^2+35x+15$
- $y^2=75x^6+55x^5+13x^4+57x^3+8x^2+7x+79$
- $y^2=72x^6+13x^5+11x^4+82x^3+66x^2+57x+5$
- $y^2=66x^6+26x^5+80x^4+17x^3+49x^2+40x+60$
- $y^2=82x^6+44x^5+20x^4+80x^3+74x^2+35x+3$
- $y^2=45x^6+4x^5+72x^4+55x^3+9x^2+73x+68$
- $y^2=5x^6+28x^5+76x^4+43x^3+5x^2+73x+71$
- $y^2=22x^6+28x^5+38x^4+79x^3+50x^2+35x+46$
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 4.0.68725.1. |
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_ob | $2$ | (not in LMFDB) |