Properties

Label 6930.c
Number of curves 2
Conductor 6930
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6930.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.c1 6930a1 [1, -1, 0, -188340, -31409200] [2] 43008 \(\Gamma_0(N)\)-optimal
6930.c2 6930a2 [1, -1, 0, -171060, -37419184] [2] 86016  

Rank

sage: E.rank()
 

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

Modular form 6930.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - q^{11} - 4q^{13} - q^{14} + q^{16} + 2q^{17} - 6q^{19} + O(q^{20}) \)

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.