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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 4560.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4560.u1 | 4560v2 | \([0, 1, 0, -3476, -72360]\) | \(18148802937424/1947796875\) | \(498636000000\) | \([2]\) | \(4608\) | \(0.97878\) | |
| 4560.u2 | 4560v1 | \([0, 1, 0, -3381, -76806]\) | \(267219216891904/3655125\) | \(58482000\) | \([2]\) | \(2304\) | \(0.63221\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.u have rank \(1\).
Complex multiplication
The elliptic curves in class 4560.u do not have complex multiplication.Modular form 4560.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
