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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 402930.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
402930.y1 | 402930y2 | \([1, -1, 0, -58360440, 171617556006]\) | \(345287978544439377/1069531250\) | \(68091266017525781250\) | \([2]\) | \(47579136\) | \(3.0318\) | \(\Gamma_0(N)\)-optimal* |
402930.y2 | 402930y1 | \([1, -1, 0, -3696270, 2606875200]\) | \(87723693730737/4685402500\) | \(298294218169576942500\) | \([2]\) | \(23789568\) | \(2.6852\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 402930.y have rank \(0\).
Complex multiplication
The elliptic curves in class 402930.y do not have complex multiplication.Modular form 402930.2.a.y
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.