Properties

Label 6930.m
Number of curves 4
Conductor 6930
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6930.m1")
sage: E.isogeny_class()

Elliptic curves in class 6930.m

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.m1 6930m3 [1, -1, 0, -296919, -62198825] 2 49152  
6930.m2 6930m2 [1, -1, 0, -19089, -909527] 4 24576  
6930.m3 6930m1 [1, -1, 0, -4509, 102325] 2 12288 \(\Gamma_0(N)\)-optimal
6930.m4 6930m4 [1, -1, 0, 25461, -4553717] 2 49152  

Rank

sage: E.rank()

The elliptic curves in class 6930.m have rank \(0\).

Modular form 6930.2.a.m

sage: E.q_eigenform(10)
\( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + q^{11} + 2q^{13} + q^{14} + q^{16} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.