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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 41280j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41280.k4 | 41280j1 | \([0, -1, 0, -76, 14350]\) | \(-768575296/1384614405\) | \(-88615321920\) | \([2]\) | \(36864\) | \(0.77960\) | \(\Gamma_0(N)\)-optimal |
| 41280.k3 | 41280j2 | \([0, -1, 0, -9321, 345321]\) | \(21867436817344/303282225\) | \(1242243993600\) | \([2, 2]\) | \(73728\) | \(1.1262\) | |
| 41280.k2 | 41280j3 | \([0, -1, 0, -17921, -382239]\) | \(19426060200968/9255045015\) | \(303269315051520\) | \([2]\) | \(147456\) | \(1.4728\) | |
| 41280.k1 | 41280j4 | \([0, -1, 0, -148641, 22107105]\) | \(11083898859981128/2176875\) | \(71331840000\) | \([2]\) | \(147456\) | \(1.4728\) |
Rank
sage: E.rank()
The elliptic curves in class 41280j have rank \(0\).
Complex multiplication
The elliptic curves in class 41280j 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 Cremona 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 Cremona labels.
