Invariants
| Base field: | $\F_{97}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 16 x + 97 x^{2} )^{2}$ |
| $1 - 32 x + 450 x^{2} - 3104 x^{3} + 9409 x^{4}$ | |
| Frobenius angles: | $\pm0.198227810371$, $\pm0.198227810371$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $26$ |
This isogeny class is not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $6724$ | $87385104$ | $833996338756$ | $7840085270593536$ | $73745594591001372484$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $66$ | $9286$ | $913794$ | $88559230$ | $8587710786$ | $832975028422$ | $80798296912770$ | $7837433500052734$ | $760231055939215938$ | $73742412655196687686$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 26 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=60x^6+44x^5+78x^4+58x^3+69x^2+47x+81$
- $y^2=28x^6+48x^5+31x^4+81x^3+31x^2+48x+28$
- $y^2=69x^6+89x^5+34x^4+61x^3+38x^2+86x+34$
- $y^2=62x^6+37x^5+84x^4+10x^3+20x^2+52x+67$
- $y^2=5x^6+76x^3+68$
- $y^2=78x^6+38x^4+38x^2+78$
- $y^2=42x^6+2x^5+53x^4+77x^3+90x^2+93x+44$
- $y^2=80x^6+62x^5+90x^4+68x^3+90x^2+62x+80$
- $y^2=49x^6+46x^5+3x^4+53x^3+80x^2+43x+30$
- $y^2=28x^6+51x^5+64x^4+33x^3+64x^2+51x+28$
- $y^2=45x^6+32x^5+32x^4+23x^3+32x^2+32x+45$
- $y^2=23x^6+22x^4+22x^2+23$
- $y^2=20x^6+72x^5+79x^4+19x^3+36x^2+37x+76$
- $y^2=6x^6+64x^5+65x^4+33x^3+65x^2+64x+6$
- $y^2=5x^6+5x^3+92$
- $y^2=74x^6+3x^5+30x^4+70x^3+95x^2+81x+86$
- $y^2=76x^6+59x^5+63x^4+4x^3+82x^2+26x+17$
- $y^2=41x^6+80x^5+22x^4+66x^3+48x^2+23x+53$
- $y^2=62x^6+43x^5+14x^4+20x^3+14x^2+43x+62$
- $y^2=45x^6+33x^5+36x^4+40x^3+58x^2+80x+28$
- $y^2=72x^6+96x^5+34x^4+58x^3+90x^2+33x+92$
- $y^2=43x^6+38x^5+15x^4+77x^3+67x^2+55x+44$
- $y^2=38x^6+67x^5+79x^4+54x^3+20x^2+7x+92$
- $y^2=87x^6+56x^5+5x^4+83x^3+84x^2+47x+3$
- $y^2=14x^6+55x^5+70x^4+3x^3+54x^2+26x+82$
- $y^2=47x^6+2x^5+36x^4+89x^3+71x^2+29x+83$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{97}$.
Endomorphism algebra over $\F_{97}$| The isogeny class factors as 1.97.aq 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-33}) \)$)$ |
Base change
This is a primitive isogeny class.