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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 11550.cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11550.cl1 | 11550ci3 | \([1, 0, 0, -304588, 64388792]\) | \(200005594092187129/1027287538200\) | \(16051367784375000\) | \([2]\) | \(147456\) | \(1.9555\) | |
11550.cl2 | 11550ci2 | \([1, 0, 0, -29588, -236208]\) | \(183337554283129/104587560000\) | \(1634180625000000\) | \([2, 2]\) | \(73728\) | \(1.6090\) | |
11550.cl3 | 11550ci1 | \([1, 0, 0, -21588, -1220208]\) | \(71210194441849/165580800\) | \(2587200000000\) | \([2]\) | \(36864\) | \(1.2624\) | \(\Gamma_0(N)\)-optimal |
11550.cl4 | 11550ci4 | \([1, 0, 0, 117412, -1853208]\) | \(11456208593737991/6725709375000\) | \(-105089208984375000\) | \([2]\) | \(147456\) | \(1.9555\) |
Rank
sage: E.rank()
The elliptic curves in class 11550.cl have rank \(0\).
Complex multiplication
The elliptic curves in class 11550.cl do not have complex multiplication.Modular form 11550.2.a.cl
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.