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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2496k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2496.q4 | 2496k1 | \([0, 1, 0, 31, -129]\) | \(12167/39\) | \(-10223616\) | \([2]\) | \(512\) | \(0.028207\) | \(\Gamma_0(N)\)-optimal |
| 2496.q3 | 2496k2 | \([0, 1, 0, -289, -1729]\) | \(10218313/1521\) | \(398721024\) | \([2, 2]\) | \(1024\) | \(0.37478\) | |
| 2496.q1 | 2496k3 | \([0, 1, 0, -4449, -115713]\) | \(37159393753/1053\) | \(276037632\) | \([2]\) | \(2048\) | \(0.72135\) | |
| 2496.q2 | 2496k4 | \([0, 1, 0, -1249, 14975]\) | \(822656953/85683\) | \(22461284352\) | \([2]\) | \(2048\) | \(0.72135\) |
Rank
sage: E.rank()
The elliptic curves in class 2496k have rank \(0\).
Complex multiplication
The elliptic curves in class 2496k do not have complex multiplication.Modular form 2496.2.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 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.
