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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 109551k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 109551.b4 | 109551k1 | \([1, 0, 0, 1346, -40381]\) | \(12167/39\) | \(-864410084031\) | \([2]\) | \(149760\) | \(0.97363\) | \(\Gamma_0(N)\)-optimal |
| 109551.b3 | 109551k2 | \([1, 0, 0, -12699, -475776]\) | \(10218313/1521\) | \(33711993277209\) | \([2, 2]\) | \(299520\) | \(1.3202\) | |
| 109551.b2 | 109551k3 | \([1, 0, 0, -54834, 4470873]\) | \(822656953/85683\) | \(1899108954616107\) | \([2]\) | \(599040\) | \(1.6668\) | |
| 109551.b1 | 109551k4 | \([1, 0, 0, -195284, -33231525]\) | \(37159393753/1053\) | \(23339072268837\) | \([2]\) | \(599040\) | \(1.6668\) |
Rank
sage: E.rank()
The elliptic curves in class 109551k have rank \(1\).
Complex multiplication
The elliptic curves in class 109551k do not have complex multiplication.Modular form 109551.2.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 Cremona 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 Cremona labels.
