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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 160080.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
160080.o1 | 160080bz2 | \([0, -1, 0, -805096, -97358480]\) | \(14089880519208782569/7148643285375000\) | \(29280842896896000000\) | \([2]\) | \(5529600\) | \(2.4278\) | |
160080.o2 | 160080bz1 | \([0, -1, 0, -649576, -201121424]\) | \(7400385515776624489/7246965672000\) | \(29683571392512000\) | \([2]\) | \(2764800\) | \(2.0812\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 160080.o have rank \(2\).
Complex multiplication
The elliptic curves in class 160080.o do not have complex multiplication.Modular form 160080.2.a.o
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.