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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 183150.fk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 183150.fk1 | 183150by4 | \([1, -1, 1, -243134555, 1459271943447]\) | \(139545621883503188502625/220644468\) | \(2513278393312500\) | \([2]\) | \(23887872\) | \(3.1118\) | |
| 183150.fk2 | 183150by3 | \([1, -1, 1, -15196055, 22803516447]\) | \(34069730739753390625/1354703543952\) | \(15430920055328250000\) | \([2]\) | \(11943936\) | \(2.7652\) | |
| 183150.fk3 | 183150by2 | \([1, -1, 1, -3010055, 1990656447]\) | \(264788619837198625/3058196150592\) | \(34834765527837000000\) | \([2]\) | \(7962624\) | \(2.5625\) | |
| 183150.fk4 | 183150by1 | \([1, -1, 1, -346055, -28655553]\) | \(402355893390625/201513996288\) | \(2295370363968000000\) | \([2]\) | \(3981312\) | \(2.2159\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 183150.fk have rank \(1\).
Complex multiplication
The elliptic curves in class 183150.fk do not have complex multiplication.Modular form 183150.2.a.fk
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.
