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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2448.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2448.k1 | 2448q4 | \([0, 0, 0, -16275, -552238]\) | \(159661140625/48275138\) | \(144148789665792\) | \([2]\) | \(6912\) | \(1.4219\) | |
| 2448.k2 | 2448q3 | \([0, 0, 0, -14835, -695374]\) | \(120920208625/19652\) | \(58680557568\) | \([2]\) | \(3456\) | \(1.0754\) | |
| 2448.k3 | 2448q2 | \([0, 0, 0, -6195, 187634]\) | \(8805624625/2312\) | \(6903595008\) | \([2]\) | \(2304\) | \(0.87263\) | |
| 2448.k4 | 2448q1 | \([0, 0, 0, -435, 2162]\) | \(3048625/1088\) | \(3248750592\) | \([2]\) | \(1152\) | \(0.52606\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2448.k have rank \(0\).
Complex multiplication
The elliptic curves in class 2448.k do not have complex multiplication.Modular form 2448.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
