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SageMath
sage: E = EllipticCurve("bm1")
sage: E.isogeny_class()
Elliptic curves in class 97020bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 97020.k2 | 97020bm1 | [0, 0, 0, -588, 88837] | [2] | 147456 | \(\Gamma_0(N)\)-optimal |
| 97020.k1 | 97020bm2 | [0, 0, 0, -33663, 2357782] | [2] | 294912 |
Rank
sage: E.rank()
The elliptic curves in class 97020bm have rank \(0\).
Complex multiplication
The elliptic curves in class 97020bm do not have complex multiplication.Modular form 97020.2.a.bm
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 Cremona 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 Cremona labels.
