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SageMath
E = EllipticCurve("gy1")
E.isogeny_class()
Elliptic curves in class 235950.gy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235950.gy1 | 235950gy3 | \([1, 0, 0, -19617188, 33438530742]\) | \(30161840495801041/2799263610\) | \(77485410003050156250\) | \([2]\) | \(23592960\) | \(2.8546\) | |
| 235950.gy2 | 235950gy4 | \([1, 0, 0, -7214688, -7091326758]\) | \(1500376464746641/83599963590\) | \(2314100548397874843750\) | \([2]\) | \(23592960\) | \(2.8546\) | |
| 235950.gy3 | 235950gy2 | \([1, 0, 0, -1315938, 441376992]\) | \(9104453457841/2226896100\) | \(61641910653314062500\) | \([2, 2]\) | \(11796480\) | \(2.5080\) | |
| 235950.gy4 | 235950gy1 | \([1, 0, 0, 196562, 43589492]\) | \(30342134159/47190000\) | \(-1306249431093750000\) | \([2]\) | \(5898240\) | \(2.1614\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.gy have rank \(1\).
Complex multiplication
The elliptic curves in class 235950.gy do not have complex multiplication.Modular form 235950.2.a.gy
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
