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SageMath
sage: E = EllipticCurve("u1")
sage: E.isogeny_class()
Elliptic curves in class 97020.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 97020.u1 | 97020bz1 | [0, 0, 0, -273, 1757] | [] | 31104 | \(\Gamma_0(N)\)-optimal |
| 97020.u2 | 97020bz2 | [0, 0, 0, 987, 8813] | [] | 93312 |
Rank
sage: E.rank()
The elliptic curves in class 97020.u have rank \(1\).
Complex multiplication
The elliptic curves in class 97020.u do not have complex multiplication.Modular form 97020.2.a.u
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.
