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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 58080.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58080.u1 | 58080bo4 | \([0, -1, 0, -19400, 1046520]\) | \(890277128/15\) | \(13605588480\) | \([2]\) | \(92160\) | \(1.0748\) | |
| 58080.u2 | 58080bo3 | \([0, -1, 0, -4880, -113628]\) | \(14172488/1875\) | \(1700698560000\) | \([2]\) | \(92160\) | \(1.0748\) | |
| 58080.u3 | 58080bo1 | \([0, -1, 0, -1250, 15600]\) | \(1906624/225\) | \(25510478400\) | \([2, 2]\) | \(46080\) | \(0.72818\) | \(\Gamma_0(N)\)-optimal |
| 58080.u4 | 58080bo2 | \([0, -1, 0, 1775, 76705]\) | \(85184/405\) | \(-2938807111680\) | \([2]\) | \(92160\) | \(1.0748\) |
Rank
sage: E.rank()
The elliptic curves in class 58080.u have rank \(0\).
Complex multiplication
The elliptic curves in class 58080.u do not have complex multiplication.Modular form 58080.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
