Invariants
Base field: | $\F_{97}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 32 x + 438 x^{2} - 3104 x^{3} + 9409 x^{4}$ |
Frobenius angles: | $\pm0.0490723411848$, $\pm0.280417090425$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.76032.2 |
Galois group: | $D_{4}$ |
Jacobians: | $28$ |
Isomorphism classes: | 44 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $6712$ | $87148608$ | $832941755512$ | $7837620123116544$ | $73741752916680318712$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $66$ | $9262$ | $912642$ | $88531390$ | $8587263426$ | $832969916206$ | $80798258135682$ | $7837433407959550$ | $760231058466706242$ | $73742412703018060462$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=2x^6+59x^5+22x^4+71x^3+91x^2+89x+82$
- $y^2=63x^6+70x^5+33x^4+30x^3+78x^2+81x+12$
- $y^2=32x^6+13x^5+49x^4+81x^3+6x^2+25x+28$
- $y^2=64x^6+85x^5+78x^4+49x^3+33x^2+13x+20$
- $y^2=21x^6+18x^5+40x^4+48x^3+20x^2+66x+68$
- $y^2=68x^6+12x^5+31x^4+10x^3+49x^2+72x+23$
- $y^2=83x^6+24x^5+92x^4+13x^3+2x^2+57x+73$
- $y^2=20x^6+25x^5+84x^4+16x^3+50x^2+25x+60$
- $y^2=78x^6+49x^5+96x^4+11x^3+46x^2+75x+90$
- $y^2=79x^6+7x^5+55x^4+19x^3+30x^2+48x+96$
- $y^2=34x^6+83x^5+47x^4+32x^3+89x^2+39x+90$
- $y^2=62x^6+46x^5+15x^4+62x^3+68x^2+21x+62$
- $y^2=68x^6+55x^5+89x^4+55x^3+34x^2+81x+89$
- $y^2=20x^6+75x^5+52x^4+71x^3+94x^2+37x+56$
- $y^2=39x^6+43x^5+67x^4+64x^3+53x^2+70x+22$
- $y^2=39x^6+43x^5+83x^4+5x^3+13x^2+21x+20$
- $y^2=55x^6+6x^5+19x^4+17x^3+51x^2+2x+7$
- $y^2=92x^6+63x^5+52x^4+18x^3+30x^2+23x+34$
- $y^2=57x^6+19x^5+60x^4+13x^2+49x+51$
- $y^2=91x^6+87x^5+72x^4+43x^3+30x^2+40x+37$
- $y^2=91x^6+69x^5+54x^4+69x^3+93x^2+53x+78$
- $y^2=23x^6+44x^5+2x^4+71x^3+40x^2+32x+66$
- $y^2=10x^6+62x^5+25x^4+48x^3+75x^2+73x+10$
- $y^2=68x^6+20x^5+27x^4+85x^3+52x^2+37x+71$
- $y^2=49x^6+85x^5+21x^4+88x^3+64x^2+89x+53$
- $y^2=40x^6+19x^5+52x^4+26x^3+39x^2+92x+66$
- $y^2=44x^6+43x^5+78x^4+44x^3+11x^2+33x+7$
- $y^2=5x^6+45x^5+72x^4+33x^3+90x^2+39x+87$
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 4.0.76032.2. |
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_qw | $2$ | (not in LMFDB) |