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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 9240.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9240.k1 | 9240g3 | \([0, -1, 0, -560695800, 5110381564092]\) | \(19037313645387618625546168804/82399233032965368135\) | \(84376814625756536970240\) | \([4]\) | \(1892352\) | \(3.6061\) | |
| 9240.k2 | 9240g2 | \([0, -1, 0, -35597100, 77205504852]\) | \(19486220601593009351102416/1221175284018082695225\) | \(312620872708629169977600\) | \([2, 2]\) | \(946176\) | \(3.2595\) | |
| 9240.k3 | 9240g1 | \([0, -1, 0, -6773095, -5300327060]\) | \(2147658844706816042407936/483688189481299210485\) | \(7739011031700787367760\) | \([2]\) | \(473088\) | \(2.9129\) | \(\Gamma_0(N)\)-optimal |
| 9240.k4 | 9240g4 | \([0, -1, 0, 28317520, 323941503900]\) | \(2452389160534358561651516/45692546768053107181875\) | \(-46789167890486381754240000\) | \([2]\) | \(1892352\) | \(3.6061\) |
Rank
sage: E.rank()
The elliptic curves in class 9240.k have rank \(1\).
Complex multiplication
The elliptic curves in class 9240.k do not have complex multiplication.Modular form 9240.2.a.k
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.
