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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 243360.dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 243360.dl1 | 243360dl1 | \([0, 0, 0, -16107897, 24837937436]\) | \(2052450196928704/4317958125\) | \(972402445606592520000\) | \([2]\) | \(12386304\) | \(2.9123\) | \(\Gamma_0(N)\)-optimal |
| 243360.dl2 | 243360dl2 | \([0, 0, 0, -10563852, 42193015904]\) | \(-9045718037056/48125390625\) | \(-693620400158337600000000\) | \([2]\) | \(24772608\) | \(3.2588\) |
Rank
sage: E.rank()
The elliptic curves in class 243360.dl have rank \(0\).
Complex multiplication
The elliptic curves in class 243360.dl do not have complex multiplication.Modular form 243360.2.a.dl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
