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SageMath
sage: E = EllipticCurve("320.f1")
sage: E.isogeny_class()
Elliptic curves in class 320.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
320.f1 | 320c3 | [0, -1, 0, -165, -763] | [2] | 48 | |
320.f2 | 320c4 | [0, -1, 0, -145, -975] | [2] | 96 | |
320.f3 | 320c1 | [0, -1, 0, -5, 5] | [2] | 16 | \(\Gamma_0(N)\)-optimal |
320.f4 | 320c2 | [0, -1, 0, 15, 17] | [2] | 32 |
Rank
sage: E.rank()
The elliptic curves in class 320.f have rank \(0\).
Modular form 320.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.