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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 221880.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221880.d1 | 221880bc3 | \([0, -1, 0, -14718656, 699685500]\) | \(54477543627364/31494140625\) | \(203863958330250000000000\) | \([2]\) | \(17031168\) | \(3.1621\) | |
| 221880.d2 | 221880bc2 | \([0, -1, 0, -9948236, -12033519564]\) | \(67283921459536/260015625\) | \(420775209993636000000\) | \([2, 2]\) | \(8515584\) | \(2.8156\) | |
| 221880.d3 | 221880bc1 | \([0, -1, 0, -9938991, -12057083220]\) | \(1073544204384256/16125\) | \(1630911666642000\) | \([2]\) | \(4257792\) | \(2.4690\) | \(\Gamma_0(N)\)-optimal |
| 221880.d4 | 221880bc4 | \([0, -1, 0, -5325736, -23258798564]\) | \(-2580786074884/34615360125\) | \(-224067848624131093632000\) | \([2]\) | \(17031168\) | \(3.1621\) |
Rank
sage: E.rank()
The elliptic curves in class 221880.d have rank \(0\).
Complex multiplication
The elliptic curves in class 221880.d do not have complex multiplication.Modular form 221880.2.a.d
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.
