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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 94640.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.be1 | 94640cx3 | \([0, -1, 0, -355125, 85328125]\) | \(-250523582464/13671875\) | \(-270301304000000000\) | \([]\) | \(886464\) | \(2.1031\) | |
| 94640.be2 | 94640cx1 | \([0, -1, 0, -3605, -91235]\) | \(-262144/35\) | \(-691971338240\) | \([]\) | \(98496\) | \(1.0045\) | \(\Gamma_0(N)\)-optimal |
| 94640.be3 | 94640cx2 | \([0, -1, 0, 23435, 227837]\) | \(71991296/42875\) | \(-847664889344000\) | \([]\) | \(295488\) | \(1.5538\) |
Rank
sage: E.rank()
The elliptic curves in class 94640.be have rank \(0\).
Complex multiplication
The elliptic curves in class 94640.be do not have complex multiplication.Modular form 94640.2.a.be
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
