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SageMath
sage: E = EllipticCurve("33620.a1")
sage: E.isogeny_class()
Elliptic curves in class 33620a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 33620.a3 | 33620a1 | [0, -1, 0, -2241, 28826] | [2] | 34560 | \(\Gamma_0(N)\)-optimal |
| 33620.a4 | 33620a2 | [0, -1, 0, 6164, 186840] | [2] | 69120 | |
| 33620.a1 | 33620a3 | [0, -1, 0, -69481, -7024650] | [2] | 103680 | |
| 33620.a2 | 33620a4 | [0, -1, 0, -61076, -8796424] | [2] | 207360 |
Rank
sage: E.rank()
The elliptic curves in class 33620a have rank \(0\).
Modular form 33620.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
