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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 94640z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.j1 | 94640z1 | \([0, 1, 0, -607780, -182371812]\) | \(20093868785104/26374985\) | \(32590595833053440\) | \([2]\) | \(1290240\) | \(2.0753\) | \(\Gamma_0(N)\)-optimal |
| 94640.j2 | 94640z2 | \([0, 1, 0, -442160, -283797500]\) | \(-1934207124196/5912841025\) | \(-29225117977640166400\) | \([2]\) | \(2580480\) | \(2.4218\) |
Rank
sage: E.rank()
The elliptic curves in class 94640z have rank \(0\).
Complex multiplication
The elliptic curves in class 94640z do not have complex multiplication.Modular form 94640.2.a.z
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.
