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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 18496.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18496.k1 | 18496j3 | \([0, 0, 0, -1677356, 836153296]\) | \(82483294977/17\) | \(107567821094912\) | \([2]\) | \(147456\) | \(2.0797\) | |
| 18496.k2 | 18496j2 | \([0, 0, 0, -105196, 12970320]\) | \(20346417/289\) | \(1828652958613504\) | \([2, 2]\) | \(73728\) | \(1.7331\) | |
| 18496.k3 | 18496j1 | \([0, 0, 0, -12716, -235824]\) | \(35937/17\) | \(107567821094912\) | \([2]\) | \(36864\) | \(1.3865\) | \(\Gamma_0(N)\)-optimal |
| 18496.k4 | 18496j4 | \([0, 0, 0, -12716, 34980560]\) | \(-35937/83521\) | \(-528480705039302656\) | \([2]\) | \(147456\) | \(2.0797\) |
Rank
sage: E.rank()
The elliptic curves in class 18496.k have rank \(0\).
Complex multiplication
The elliptic curves in class 18496.k do not have complex multiplication.Modular form 18496.2.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.
