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SageMath
sage: E = EllipticCurve("6930.n1")
sage: E.isogeny_class()
Elliptic curves in class 6930.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
6930.n1 | 6930e4 | [1, -1, 0, -40839, -2960515] | [2] | 41472 | |
6930.n2 | 6930e2 | [1, -1, 0, -7764, 264420] | [6] | 13824 | |
6930.n3 | 6930e1 | [1, -1, 0, -264, 7920] | [6] | 6912 | \(\Gamma_0(N)\)-optimal |
6930.n4 | 6930e3 | [1, -1, 0, 2361, -204355] | [2] | 20736 |
Rank
sage: E.rank()
The elliptic curves in class 6930.n have rank \(1\).
Modular form 6930.2.a.n
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.