Invariants
Base field: | $\F_{97}$ |
Dimension: | $2$ |
L-polynomial: | $1 + 8 x + 202 x^{2} + 776 x^{3} + 9409 x^{4}$ |
Frobenius angles: | $\pm0.518943488750$, $\pm0.612684523000$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.527936.1 |
Galois group: | $D_{4}$ |
Jacobians: | $220$ |
Isomorphism classes: | 280 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $10396$ | $91775888$ | $831141747100$ | $7835558066054144$ | $73744439397538819996$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $106$ | $9750$ | $910666$ | $88508094$ | $8587576266$ | $832972755990$ | $80798266131178$ | $7837433605654014$ | $760231059467008042$ | $73742412687885817750$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 220 curves (of which all are hyperelliptic):
- $y^2=3 x^6+83 x^5+91 x^4+42 x^3+94 x^2+62 x+62$
- $y^2=9 x^6+x^5+54 x^4+84 x^3+71 x^2+29 x$
- $y^2=69 x^6+86 x^5+81 x^4+34 x^3+3 x^2+72$
- $y^2=33 x^6+55 x^5+74 x^4+x^3+81 x^2+2 x+90$
- $y^2=72 x^6+68 x^5+75 x^4+12 x^3+29 x^2+3 x+39$
- $y^2=83 x^6+51 x^5+21 x^4+86 x^3+32 x^2+2 x+82$
- $y^2=96 x^6+89 x^5+49 x^4+69 x^3+72 x^2+67 x+88$
- $y^2=84 x^6+85 x^5+54 x^4+48 x^3+86 x^2+86 x+93$
- $y^2=6 x^6+92 x^5+65 x^4+57 x^3+27 x^2+28 x+66$
- $y^2=10 x^6+49 x^5+35 x^4+10 x^3+73 x^2+11 x+84$
- $y^2=57 x^6+12 x^5+46 x^4+48 x^3+87 x^2+89 x+1$
- $y^2=11 x^6+50 x^5+10 x^4+50 x^3+88 x^2+67 x+95$
- $y^2=6 x^6+13 x^5+62 x^4+43 x^3+61 x^2+3 x+33$
- $y^2=14 x^6+32 x^5+16 x^4+87 x^3+23 x^2+64 x+17$
- $y^2=76 x^6+8 x^5+51 x^4+48 x^3+33 x^2+44 x+81$
- $y^2=63 x^6+10 x^5+5 x^4+17 x^3+38 x^2+72 x+24$
- $y^2=21 x^6+23 x^5+10 x^4+92 x^3+17 x^2+76 x+42$
- $y^2=82 x^6+62 x^5+13 x^4+18 x^3+30 x^2+56$
- $y^2=34 x^6+14 x^5+12 x^4+68 x^3+93 x^2+62 x+49$
- $y^2=12 x^6+47 x^5+15 x^4+53 x^3+72 x^2+49 x+66$
- and 200 more
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 4.0.527936.1. |
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.ai_hu | $2$ | (not in LMFDB) |