Invariants
Base field: | $\F_{97}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 33 x + 459 x^{2} - 3201 x^{3} + 9409 x^{4}$ |
Frobenius angles: | $\pm0.0722424791852$, $\pm0.252752713219$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.3260557.1 |
Galois group: | $D_{4}$ |
Jacobians: | $21$ |
Isomorphism classes: | 21 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $6635$ | $86938405$ | $832881418355$ | $7838073177683125$ | $73742816233156074800$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $65$ | $9239$ | $912575$ | $88536507$ | $8587387250$ | $832971531431$ | $80798271342035$ | $7837433460663763$ | $760231058313671885$ | $73742412702024267614$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 21 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=82x^6+90x^5+92x^4+49x^3+13x^2+62x+75$
- $y^2=58x^6+81x^5+66x^4+5x^3+6x^2+61x+65$
- $y^2=68x^6+86x^5+8x^4+32x^3+84x^2+25x+75$
- $y^2=24x^6+47x^5+17x^3+66x^2+56x+23$
- $y^2=47x^6+56x^5+80x^4+55x^3+23x^2+59x+91$
- $y^2=83x^6+5x^5+67x^4+60x^3+68x^2+56$
- $y^2=90x^6+15x^5+13x^4+85x^3+14x^2+81x+56$
- $y^2=10x^6+15x^5+52x^4+91x^3+95x^2+80x+82$
- $y^2=15x^6+32x^5+47x^4+11x^3+62x^2+85x+68$
- $y^2=15x^6+77x^5+80x^4+38x^3+2x^2+9x+55$
- $y^2=65x^6+69x^5+41x^4+44x^3+28x^2+87x+96$
- $y^2=60x^6+59x^5+41x^4+64x^3+87x^2+56x+6$
- $y^2=82x^6+57x^5+15x^4+41x^3+52x^2+49x+56$
- $y^2=14x^6+15x^5+64x^4+5x^3+6x^2+41x+71$
- $y^2=60x^6+59x^5+95x^4+5x^3+66x^2+43x+77$
- $y^2=50x^6+59x^5+33x^4+31x^3+87x^2+66x+90$
- $y^2=86x^6+51x^5+78x^4+29x^3+47x^2+36x+64$
- $y^2=80x^6+54x^5+84x^4+18x^3+70x^2+68x+92$
- $y^2=69x^6+27x^5+13x^4+78x^3+6x^2+93x+54$
- $y^2=69x^6+20x^5+36x^4+81x^3+82x^2+14x+89$
- $y^2=77x^6+11x^5+25x^4+24x^3+93x^2+34x+45$
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 4.0.3260557.1. |
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.bh_rr | $2$ | (not in LMFDB) |