Properties

Label 6930.k
Number of curves 2
Conductor 6930
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6930.k1")
sage: E.isogeny_class()

Elliptic curves in class 6930.k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.k1 6930d1 [1, -1, 0, -2364, 44828] 2 6144 \(\Gamma_0(N)\)-optimal
6930.k2 6930d2 [1, -1, 0, -2094, 55250] 2 12288  

Rank

sage: E.rank()

The elliptic curves in class 6930.k have rank \(1\).

Modular form 6930.2.a.k

sage: E.q_eigenform(10)
\( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + q^{11} - 6q^{13} + q^{14} + q^{16} + 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.