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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 402486.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
402486.v1 | 402486v2 | \([1, 1, 0, -160123744, 779817878848]\) | \(1504154129818033/5519808\) | \(1666182451346186171328\) | \([2]\) | \(63037440\) | \(3.2885\) | \(\Gamma_0(N)\)-optimal* |
402486.v2 | 402486v1 | \([1, 1, 0, -9862304, 12552913920]\) | \(-351447414193/22278144\) | \(-6724772416244066709504\) | \([2]\) | \(31518720\) | \(2.9419\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 402486.v have rank \(0\).
Complex multiplication
The elliptic curves in class 402486.v do not have complex multiplication.Modular form 402486.2.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.