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SageMath
sage: E = EllipticCurve("2541.j1")
sage: E.isogeny_class()
Elliptic curves in class 2541l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 2541.j6 | 2541l1 | [1, 0, 1, 118, 119] | [2] | 640 | \(\Gamma_0(N)\)-optimal |
| 2541.j5 | 2541l2 | [1, 0, 1, -487, 845] | [2, 2] | 1280 | |
| 2541.j3 | 2541l3 | [1, 0, 1, -4722, -124511] | [2] | 2560 | |
| 2541.j2 | 2541l4 | [1, 0, 1, -5932, 175085] | [2, 2] | 2560 | |
| 2541.j1 | 2541l5 | [1, 0, 1, -94867, 11238599] | [2] | 5120 | |
| 2541.j4 | 2541l6 | [1, 0, 1, -4117, 284711] | [2] | 5120 |
Rank
sage: E.rank()
The elliptic curves in class 2541l have rank \(0\).
Modular form 2541.2.a.j
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
