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SageMath
sage: E = EllipticCurve("v1")
sage: E.isogeny_class()
Elliptic curves in class 97020.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
97020.v1 | 97020bf2 | [0, 0, 0, -562863, 220176502] | [3] | 2177280 | |
97020.v2 | 97020bf1 | [0, 0, 0, 54537, -3692738] | [] | 725760 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.v have rank \(0\).
Complex multiplication
The elliptic curves in class 97020.v do not have complex multiplication.Modular form 97020.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.