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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 141610.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141610.v1 | 141610cc2 | \([1, -1, 0, -9319, -341517]\) | \(154854153/1250\) | \(722511921250\) | \([2]\) | \(276480\) | \(1.1026\) | |
141610.v2 | 141610cc1 | \([1, -1, 0, -989, 3345]\) | \(185193/100\) | \(57800953700\) | \([2]\) | \(138240\) | \(0.75607\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141610.v have rank \(1\).
Complex multiplication
The elliptic curves in class 141610.v do not have complex multiplication.Modular form 141610.2.a.v
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.