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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 87120.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
87120.y1 | 87120du2 | \([0, 0, 0, -2343, 40898]\) | \(5726576/405\) | \(100600600320\) | \([2]\) | \(73728\) | \(0.85848\) | |
87120.y2 | 87120du1 | \([0, 0, 0, 132, 2783]\) | \(16384/225\) | \(-3493076400\) | \([2]\) | \(36864\) | \(0.51191\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.y have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.y do not have complex multiplication.Modular form 87120.2.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.