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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 41280.ck
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41280.ck1 | 41280cv2 | \([0, 1, 0, -15201, 693279]\) | \(1481933914201/53916840\) | \(14133976104960\) | \([2]\) | \(110592\) | \(1.2930\) | |
41280.ck2 | 41280cv1 | \([0, 1, 0, -2401, -31201]\) | \(5841725401/1857600\) | \(486958694400\) | \([2]\) | \(55296\) | \(0.94645\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41280.ck have rank \(1\).
Complex multiplication
The elliptic curves in class 41280.ck do not have complex multiplication.Modular form 41280.2.a.ck
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.