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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 468270.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
468270.v1 | 468270v2 | \([1, -1, 0, -258660, -48951864]\) | \(1481933914201/53916840\) | \(69631871849697960\) | \([2]\) | \(6451200\) | \(2.0016\) | |
468270.v2 | 468270v1 | \([1, -1, 0, -40860, 2144016]\) | \(5841725401/1857600\) | \(2399030899214400\) | \([2]\) | \(3225600\) | \(1.6550\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 468270.v have rank \(2\).
Complex multiplication
The elliptic curves in class 468270.v do not have complex multiplication.Modular form 468270.2.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.