Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 31 x + 402 x^{2} - 2573 x^{3} + 6889 x^{4}$ |
Frobenius angles: | $\pm0.0858905147336$, $\pm0.235991757082$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.258077.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
Isomorphism classes: | 12 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4688$ | $46392448$ | $326869656128$ | $2252627436982784$ | $15516350009006779888$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $53$ | $6733$ | $571664$ | $47465385$ | $3939119043$ | $326940726934$ | $27136049461049$ | $2252292195683985$ | $186940255121551856$ | $15516041190966405213$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=57x^5+51x^4+65x^3+x^2+55x+76$
- $y^2=64x^6+44x^5+53x^4+48x^3+82x^2+38x+74$
- $y^2=7x^6+70x^5+66x^4+54x^3+71x^2+25x+7$
- $y^2=22x^6+55x^5+49x^4+50x^3+24x^2+14x+66$
- $y^2=24x^6+9x^5+22x^4+45x^3+x^2+79x+48$
- $y^2=39x^6+x^5+77x^4+25x^3+28x^2+5x+76$
- $y^2=82x^6+27x^5+69x^4+75x^3+74x^2+38x+74$
- $y^2=54x^6+9x^5+59x^4+22x^3+44x^2+23x+82$
- $y^2=82x^6+5x^5+2x^4+74x^3+21x^2+48x+6$
- $y^2=24x^6+52x^5+18x^4+81x^3+58x^2+41x+48$
- $y^2=46x^6+53x^5+40x^4+51x^3+18x^2+60x+55$
- $y^2=46x^6+10x^5+70x^4+18x^3+x^2+80x+43$
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 4.0.258077.1. |
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.bf_pm | $2$ | (not in LMFDB) |