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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 4560.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4560.s1 | 4560x3 | \([0, 1, 0, -9936, 377364]\) | \(26487576322129/44531250\) | \(182400000000\) | \([2]\) | \(6144\) | \(1.0561\) | |
| 4560.s2 | 4560x2 | \([0, 1, 0, -816, 1620]\) | \(14688124849/8122500\) | \(33269760000\) | \([2, 2]\) | \(3072\) | \(0.70949\) | |
| 4560.s3 | 4560x1 | \([0, 1, 0, -496, -4396]\) | \(3301293169/22800\) | \(93388800\) | \([2]\) | \(1536\) | \(0.36292\) | \(\Gamma_0(N)\)-optimal |
| 4560.s4 | 4560x4 | \([0, 1, 0, 3184, 16020]\) | \(871257511151/527800050\) | \(-2161869004800\) | \([4]\) | \(6144\) | \(1.0561\) |
Rank
sage: E.rank()
The elliptic curves in class 4560.s have rank \(0\).
Complex multiplication
The elliptic curves in class 4560.s do not have complex multiplication.Modular form 4560.2.a.s
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
