Properties

Label 6930.b
Number of curves 4
Conductor 6930
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6930.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.b1 6930f3 [1, -1, 0, -443520, 113799816] [2] 24576  
6930.b2 6930f2 [1, -1, 0, -27720, 1783296] [2, 2] 12288  
6930.b3 6930f4 [1, -1, 0, -26640, 1927800] [2] 24576  
6930.b4 6930f1 [1, -1, 0, -1800, 25920] [2] 6144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 6930.2.a.b

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.