Properties

Label 6930.a
Number of curves 6
Conductor 6930
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6930.a1")
sage: E.isogeny_class()

Elliptic curves in class 6930.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.a1 6930g5 [1, -1, 0, -426105, 107150665] 2 65536  
6930.a2 6930g3 [1, -1, 0, -177525, -28745339] 2 32768  
6930.a3 6930g4 [1, -1, 0, -29205, 1337125] 4 32768  
6930.a4 6930g2 [1, -1, 0, -11205, -437675] 4 16384  
6930.a5 6930g1 [1, -1, 0, 315, -25259] 2 8192 \(\Gamma_0(N)\)-optimal
6930.a6 6930g6 [1, -1, 0, 79695, 8894785] 2 65536  

Rank

sage: E.rank()

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

Modular form 6930.2.a.a

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.