Invariants
Base field: | $\F_{97}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 31 x + 419 x^{2} - 3007 x^{3} + 9409 x^{4}$ |
Frobenius angles: | $\pm0.0549321449374$, $\pm0.299663331143$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.10794621.1 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
Isomorphism classes: | 8 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $6791$ | $87379797$ | $833112280871$ | $7837500920644629$ | $73741386210244305776$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $67$ | $9287$ | $912829$ | $88530043$ | $8587220722$ | $832969603847$ | $80798260960057$ | $7837433504765971$ | $760231059635348023$ | $73742412709317090782$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=54x^6+20x^5+81x^4+28x^3+35x^2+60x+88$
- $y^2=23x^6+74x^5+22x^4+68x^3+43x^2+82x+95$
- $y^2=90x^6+81x^5+53x^4+88x^3+66x^2+57x+10$
- $y^2=19x^6+75x^5+65x^4+32x^3+37x^2+96x+28$
- $y^2=15x^6+78x^5+75x^4+8x^3+40x^2+58x+95$
- $y^2=90x^6+88x^5+88x^4+73x^3+49x^2+87x+38$
- $y^2=32x^6+93x^5+7x^4+27x^3+4x^2+2x+33$
- $y^2=5x^6+44x^5+55x^4+43x^3+73x^2+67x+6$
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 4.0.10794621.1. |
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.bf_qd | $2$ | (not in LMFDB) |