Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 41 x + 691 x^{2} - 5699 x^{3} + 19321 x^{4}$ |
Frobenius angles: | $\pm0.0577546537355$, $\pm0.227538408547$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.145493.1 |
Galois group: | $D_{4}$ |
Jacobians: | $15$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14273$ | $367572569$ | $7209797036099$ | $139356731313834125$ | $2692459105608550905648$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $99$ | $19023$ | $2684595$ | $373309251$ | $51888977704$ | $7212549129411$ | $1002544331476941$ | $139353666492089331$ | $19370159734267931385$ | $2692452204154670389078$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 15 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=90x^6+2x^5+44x^4+115x^3+138x^2+41x+110$
- $y^2=77x^6+49x^5+37x^4+121x^3+36x^2+66x+88$
- $y^2=92x^6+87x^5+9x^4+92x^3+97x^2+60x+19$
- $y^2=123x^6+131x^5+40x^4+22x^3+94x^2+33x+61$
- $y^2=79x^6+9x^5+130x^4+89x^3+81x^2+86x+125$
- $y^2=95x^6+121x^5+126x^4+38x^3+25x^2+8x+86$
- $y^2=68x^6+100x^5+84x^4+117x^3+44x^2+77x+28$
- $y^2=34x^6+94x^5+58x^4+105x^3+83x^2+32x+138$
- $y^2=31x^6+58x^5+100x^4+61x^3+102x^2+73x+27$
- $y^2=119x^6+49x^5+114x^4+15x^3+14x^2+6x+60$
- $y^2=5x^6+57x^5+72x^4+22x^3+36x^2+77x+77$
- $y^2=105x^6+127x^5+114x^4+72x^3+50x^2+36x+14$
- $y^2=33x^6+92x^5+56x^4+4x^3+51x^2+60x+13$
- $y^2=86x^6+109x^5+82x^4+18x^3+34x^2+112x+7$
- $y^2=122x^6+40x^5+16x^4+3x^3+102x^2+99x+61$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{139}$.
Endomorphism algebra over $\F_{139}$The endomorphism algebra of this simple isogeny class is 4.0.145493.1. |
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 |
---|---|---|
2.139.bp_bap | $2$ | (not in LMFDB) |