Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 41 x + 693 x^{2} - 5617 x^{3} + 18769 x^{4}$ |
Frobenius angles: | $\pm0.125334691278$, $\pm0.189503359060$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.347525.1 |
Galois group: | $D_{4}$ |
Jacobians: | $11$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $13805$ | $346795405$ | $6610490027405$ | $124107569282705525$ | $2329223182564580962000$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $97$ | $18475$ | $2570821$ | $352302723$ | $48262328142$ | $6611864583475$ | $905824393318501$ | $124097930636747043$ | $17001416408198445817$ | $2329194047539600200750$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 11 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=41x^6+94x^5+70x^4+85x^3+71x^2+20x+23$
- $y^2=89x^6+128x^5+47x^4+63x^3+6x^2+49x+43$
- $y^2=85x^6+132x^5+111x^4+131x^3+102x^2+93x+77$
- $y^2=52x^6+122x^5+26x^4+50x^3+132x^2+104x+33$
- $y^2=86x^6+106x^5+96x^4+x^3+135x^2+62x+104$
- $y^2=131x^6+117x^5+43x^4+81x^3+60x^2+11x+67$
- $y^2=11x^6+62x^5+124x^4+101x^3+104x^2+3x+72$
- $y^2=98x^6+16x^5+48x^4+90x^3+43x^2+78x$
- $y^2=88x^6+72x^5+67x^4+51x^3+62x^2+8x+49$
- $y^2=83x^6+49x^5+76x^4+94x^3+71x^2+54x+83$
- $y^2=41x^6+82x^5+10x^4+119x^3+125x^2+18x+67$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{137}$.
Endomorphism algebra over $\F_{137}$The endomorphism algebra of this simple isogeny class is 4.0.347525.1. |
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 |
---|---|---|
2.137.bp_bar | $2$ | (not in LMFDB) |