Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("6930.f1")
sage: E.isogeny_class()

Elliptic curves in class 6930h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.f4 6930h1 [1, -1, 0, 90, -2700] 2 4608 \(\Gamma_0(N)\)-optimal
6930.f2 6930h2 [1, -1, 0, -2430, -43524] 2 9216  
6930.f3 6930h3 [1, -1, 0, -810, 73440] 6 13824  
6930.f1 6930h4 [1, -1, 0, -31680, 2166426] 6 27648  

Rank

sage: E.rank()

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

Modular form 6930.2.a.f

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.