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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 463680.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 463680.cs1 | 463680cs1 | \([0, 0, 0, -315302508, 900998410832]\) | \(489781415227546051766883/233890092903563264000\) | \(1655447881881015583506432000\) | \([2]\) | \(198180864\) | \(3.9167\) | \(\Gamma_0(N)\)-optimal |
| 463680.cs2 | 463680cs2 | \([0, 0, 0, 1131732372, 6852942279248]\) | \(22649115256119592694355357/15973509811739648000000\) | \(-113058713414394313703424000000\) | \([2]\) | \(396361728\) | \(4.2633\) |
Rank
sage: E.rank()
The elliptic curves in class 463680.cs have rank \(0\).
Complex multiplication
The elliptic curves in class 463680.cs do not have complex multiplication.Modular form 463680.2.a.cs
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.
