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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 86640.cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86640.cu1 | 86640cv2 | \([0, 1, 0, -148911176, 699280139124]\) | \(276288773643091/41990400\) | \(55499921427739941273600\) | \([2]\) | \(9338880\) | \(3.3768\) | |
86640.cu2 | 86640cv1 | \([0, 1, 0, -8438856, 13044761460]\) | \(-50284268371/26542080\) | \(-35081431816052901150720\) | \([2]\) | \(4669440\) | \(3.0302\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86640.cu have rank \(1\).
Complex multiplication
The elliptic curves in class 86640.cu do not have complex multiplication.Modular form 86640.2.a.cu
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.