Invariants
Base field: | $\F_{97}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 33 x + 461 x^{2} - 3201 x^{3} + 9409 x^{4}$ |
Frobenius angles: | $\pm0.0969400924774$, $\pm0.243527418132$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.2863413.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $6637$ | $86977885$ | $833062707157$ | $7838518752955125$ | $73743570038409356752$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $65$ | $9243$ | $912773$ | $88541539$ | $8587475030$ | $832972690131$ | $80798283263021$ | $7837433554480291$ | $760231058823391601$ | $73742412703119893118$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=34x^6+79x^5+25x^4+21x^3+50x^2+26x+92$
- $y^2=89x^6+92x^5+8x^4+64x^3+15x^2+6x+91$
- $y^2=83x^6+49x^5+38x^4+17x^3+65x^2+80x+78$
- $y^2=23x^6+50x^5+36x^4+23x^3+43x^2+29x+29$
- $y^2=40x^6+18x^5+66x^4+63x^3+70x^2+23x+84$
- $y^2=86x^6+47x^5+56x^4+35x^3+27x^2+49x+21$
- $y^2=73x^6+34x^5+85x^4+29x^3+43x^2+89x+5$
- $y^2=42x^6+41x^5+34x^4+76x^3+5x^2+85x+21$
- $y^2=63x^6+46x^5+25x^4+24x^3+39x^2+59x+54$
- $y^2=23x^6+8x^5+75x^4+46x^3+4x^2+85x+5$
- $y^2=74x^6+85x^5+41x^4+38x^3+4x^2+15x+11$
- $y^2=39x^6+47x^5+33x^4+64x^3+25x^2+73$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{97}$.
Endomorphism algebra over $\F_{97}$The endomorphism algebra of this simple isogeny class is 4.0.2863413.2. |
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 |
---|---|---|
2.97.bh_rt | $2$ | (not in LMFDB) |