Invariants
Base field: | $\F_{97}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 32 x + 445 x^{2} - 3104 x^{3} + 9409 x^{4}$ |
Frobenius angles: | $\pm0.123396080635$, $\pm0.253736526271$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.275225.1 |
Galois group: | $D_{4}$ |
Jacobians: | $28$ |
Isomorphism classes: | 28 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $6719$ | $87286529$ | $833556882416$ | $7839064296622361$ | $73744041973759674759$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $66$ | $9276$ | $913314$ | $88547700$ | $8587529986$ | $832973127582$ | $80798287121730$ | $7837433595013284$ | $760231059198079458$ | $73742412704244869836$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=62x^6+55x^5+26x^4+74x^3+57x^2+93x+47$
- $y^2=58x^6+95x^5+41x^4+39x^3+5x^2+37x+17$
- $y^2=56x^6+86x^5+55x^4+93x^3+24x^2+91x+9$
- $y^2=12x^6+70x^5+84x^4+83x^3+43x^2+51x+50$
- $y^2=41x^6+62x^5+33x^4+5x^3+48x^2+84x+71$
- $y^2=10x^6+25x^5+11x^4+79x^3+69x^2+95x+40$
- $y^2=15x^6+64x^5+3x^4+92x^2+53x+93$
- $y^2=10x^6+59x^5+90x^4+76x^3+41x^2+44x+77$
- $y^2=19x^6+51x^5+95x^4+96x^3+30x^2+19x+82$
- $y^2=6x^6+30x^5+34x^4+49x^3+89x^2+84x+4$
- $y^2=32x^6+84x^5+40x^4+62x^3+82x^2+83x+96$
- $y^2=30x^6+66x^5+86x^4+72x^3+57x^2+37x+37$
- $y^2=40x^6+31x^5+76x^4+66x^3+56x^2+46x+63$
- $y^2=82x^6+28x^5+33x^4+71x^3+41x^2+30x+72$
- $y^2=6x^6+93x^5+83x^4+61x^3+64x^2+20x+78$
- $y^2=77x^6+28x^5+25x^4+53x^3+91x^2+34x+79$
- $y^2=40x^6+34x^5+71x^4+74x^3+94x^2+x+80$
- $y^2=16x^6+26x^5+13x^4+46x^3+74x^2+86x+68$
- $y^2=90x^6+69x^5+68x^4+16x^2+91x+17$
- $y^2=13x^6+22x^5+50x^4+95x^3+65x^2+42x+43$
- $y^2=90x^6+78x^5+43x^4+62x^3+59x^2+37x+87$
- $y^2=78x^6+7x^5+39x^4+80x^3+5x^2+70x+83$
- $y^2=82x^6+85x^5+83x^4+x^3+24x^2+85x+14$
- $y^2=81x^6+61x^5+5x^4+33x^3+13x^2+31x+74$
- $y^2=87x^6+71x^5+36x^4+40x^3+85x^2+3x+26$
- $y^2=25x^6+79x^5+88x^4+33x^3+91x^2+32x+78$
- $y^2=20x^6+3x^5+2x^4+14x^3+38x^2+36x+64$
- $y^2=7x^6+62x^5+94x^4+21x^3+25x^2+35x+57$
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 4.0.275225.1. |
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 |
---|---|---|
2.97.bg_rd | $2$ | (not in LMFDB) |