Properties

 Label 6930.z Number of curves 8 Conductor 6930 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.z1")

sage: E.isogeny_class()

Elliptic curves in class 6930.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.z1 6930ba7 [1, -1, 1, -2307848, -1265537149] [6] 221184
6930.z2 6930ba4 [1, -1, 1, -2268023, -1314110419] [2] 73728
6930.z3 6930ba6 [1, -1, 1, -455648, 94718531] [2, 6] 110592
6930.z4 6930ba3 [1, -1, 1, -429728, 108528707] [6] 55296
6930.z5 6930ba2 [1, -1, 1, -141773, -20499919] [2, 2] 36864
6930.z6 6930ba5 [1, -1, 1, -115043, -28486843] [2] 73728
6930.z7 6930ba1 [1, -1, 1, -10553, -187063] [2] 18432 $$\Gamma_0(N)$$-optimal
6930.z8 6930ba8 [1, -1, 1, 981832, 570811907] [6] 221184

Rank

sage: E.rank()

The elliptic curves in class 6930.z have rank $$1$$.

Modular form6930.2.a.z

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} + q^{11} + 2q^{13} + q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.