Invariants
Base field: | $\F_{79}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 30 x + 378 x^{2} - 2370 x^{3} + 6241 x^{4}$ |
Frobenius angles: | $\pm0.0786820106693$, $\pm0.245045289901$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.72400.1 |
Galois group: | $D_{4}$ |
Jacobians: | $30$ |
Isomorphism classes: | 40 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4220$ | $38064400$ | $243043088780$ | $1517326766982400$ | $9468423322855755500$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $50$ | $6098$ | $492950$ | $38955678$ | $3077104250$ | $243087461138$ | $19203904891550$ | $1517108763425278$ | $119851595850620450$ | $9468276086497561298$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 30 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=58x^6+76x^5+65x^4+72x^3+39x^2+32x+38$
- $y^2=72x^6+46x^5+16x^4+2x^3+17x^2+10x+56$
- $y^2=57x^6+32x^5+20x^4+21x^3+60x^2+77x+47$
- $y^2=26x^6+33x^5+57x^4+69x^3+61x^2+55x+73$
- $y^2=59x^6+35x^5+x^4+53x^3+21x^2+x+35$
- $y^2=44x^6+72x^5+35x^4+49x^3+22x^2+60x+41$
- $y^2=x^6+47x^5+7x^4+46x^3+22x^2+15x+53$
- $y^2=77x^6+11x^5+35x^4+75x^3+55x^2+29x+24$
- $y^2=30x^6+7x^5+74x^4+21x^3+3x^2+30x+69$
- $y^2=56x^6+61x^5+58x^4+42x^3+9x^2+33x+35$
- $y^2=3x^6+69x^5+12x^4+18x^3+67x^2+75x+72$
- $y^2=69x^6+34x^5+33x^4+64x^3+x^2+20x+68$
- $y^2=12x^6+22x^5+40x^4+41x^3+62x^2+76x+39$
- $y^2=59x^6+51x^5+69x^4+41x^3+48x^2+71x+78$
- $y^2=19x^6+60x^5+61x^4+70x^3+18x^2+21x+1$
- $y^2=70x^6+8x^5+47x^4+26x^3+47x^2+2x+72$
- $y^2=24x^6+77x^5+78x^4+38x^3+3x^2+55x+40$
- $y^2=23x^6+72x^5+63x^4+47x^3+67x^2+44x+15$
- $y^2=9x^6+65x^5+67x^4+40x^3+16x^2+25x+14$
- $y^2=37x^6+78x^5+65x^4+29x^3+19x^2+78x+59$
- $y^2=71x^6+47x^5+30x^4+37x^3+39x^2+30x+52$
- $y^2=33x^6+49x^5+6x^4+12x^3+47x^2+37x+7$
- $y^2=32x^6+38x^5+11x^4+50x^3+35x^2+52x+12$
- $y^2=60x^6+71x^5+75x^4+24x^3+37x^2+15x+21$
- $y^2=58x^6+47x^5+6x^4+32x^3+77x^2+32x+33$
- $y^2=65x^6+5x^5+51x^4+74x^3+38x^2+71x+51$
- $y^2=31x^6+10x^5+65x^4+73x^3+x^2+71x+21$
- $y^2=63x^6+17x^5+64x^4+43x^3+6x^2+18x+23$
- $y^2=3x^6+39x^5+22x^4+42x^3+x^2+36x+56$
- $y^2=26x^6+10x^5+51x^4+62x^3+57x^2+58x+27$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{79}$.
Endomorphism algebra over $\F_{79}$The endomorphism algebra of this simple isogeny class is 4.0.72400.1. |
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 |
---|---|---|
2.79.be_oo | $2$ | (not in LMFDB) |