Properties

 Label 3.7.aj_bq_afd Base Field $\F_{7}$ Dimension $3$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{7}$ Dimension: $3$ L-polynomial: $1 - 9 x + 42 x^{2} - 133 x^{3} + 294 x^{4} - 441 x^{5} + 343 x^{6}$ Frobenius angles: $\pm0.0337411547966$, $\pm0.282571984656$, $\pm0.476016355688$ Angle rank: $3$ (numerical) Number field: 6.0.1714608.1 Galois group: $D_{6}$

This isogeny class is simple and geometrically simple.

Newton polygon

 $p$-rank: $1$ Slopes: $[0, 1/2, 1/2, 1/2, 1/2, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 97 122511 41003452 13303346979 4678048479367 1623844456271856 557031695003568049 191235483740749262763 65690218868207530794148 22542275480741043427678431

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 53 350 2309 16559 117320 821309 5754389 40340006 282512033

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
 The endomorphism algebra of this simple isogeny class is 6.0.1714608.1.
All geometric endomorphisms are defined over $\F_{7}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.j_bq_fd $2$ (not in LMFDB) 3.7.d_a_ah $3$ (not in LMFDB) 3.7.g_v_ce $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.7.j_bq_fd $2$ (not in LMFDB) 3.7.d_a_ah $3$ (not in LMFDB) 3.7.g_v_ce $3$ (not in LMFDB) 3.7.ag_v_ace $6$ (not in LMFDB) 3.7.ad_a_h $6$ (not in LMFDB)