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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 4950e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4950.s2 | 4950e1 | \([1, -1, 0, 4008, 402416]\) | \(185193/1936\) | \(-74426343750000\) | \([2]\) | \(19200\) | \(1.3428\) | \(\Gamma_0(N)\)-optimal |
| 4950.s1 | 4950e2 | \([1, -1, 0, -63492, 5734916]\) | \(736314327/58564\) | \(2251396898437500\) | \([2]\) | \(38400\) | \(1.6894\) |
Rank
sage: E.rank()
The elliptic curves in class 4950e have rank \(0\).
Complex multiplication
The elliptic curves in class 4950e do not have complex multiplication.Modular form 4950.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
