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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 41280.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41280.ce1 | 41280cy4 | \([0, 1, 0, -31841, 59295]\) | \(54477543627364/31494140625\) | \(2064000000000000\) | \([2]\) | \(147456\) | \(1.6281\) | |
| 41280.ce2 | 41280cy2 | \([0, 1, 0, -21521, -1218321]\) | \(67283921459536/260015625\) | \(4260096000000\) | \([2, 2]\) | \(73728\) | \(1.2815\) | |
| 41280.ce3 | 41280cy1 | \([0, 1, 0, -21501, -1220685]\) | \(1073544204384256/16125\) | \(16512000\) | \([2]\) | \(36864\) | \(0.93496\) | \(\Gamma_0(N)\)-optimal |
| 41280.ce4 | 41280cy3 | \([0, 1, 0, -11521, -2344321]\) | \(-2580786074884/34615360125\) | \(-2268552241152000\) | \([2]\) | \(147456\) | \(1.6281\) |
Rank
sage: E.rank()
The elliptic curves in class 41280.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 41280.ce do not have complex multiplication.Modular form 41280.2.a.ce
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
