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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 41280.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41280.j1 | 41280i4 | \([0, -1, 0, -990721, 379885825]\) | \(820480625548035842/5805\) | \(760872960\) | \([2]\) | \(270336\) | \(1.7585\) | |
| 41280.j2 | 41280i3 | \([0, -1, 0, -66241, 5077441]\) | \(245245463376482/57692266875\) | \(7561840803840000\) | \([2]\) | \(270336\) | \(1.7585\) | |
| 41280.j3 | 41280i2 | \([0, -1, 0, -61921, 5950945]\) | \(400649568576484/33698025\) | \(2208433766400\) | \([2, 2]\) | \(135168\) | \(1.4120\) | |
| 41280.j4 | 41280i1 | \([0, -1, 0, -3601, 107281]\) | \(-315278049616/114259815\) | \(-1872032808960\) | \([2]\) | \(67584\) | \(1.0654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41280.j have rank \(0\).
Complex multiplication
The elliptic curves in class 41280.j do not have complex multiplication.Modular form 41280.2.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 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.
