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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 466578.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466578.n1 | 466578n2 | \([1, -1, 0, -23267106, -43191987854]\) | \(-497971549873/6\) | \(-16784080231335606\) | \([]\) | \(23369472\) | \(2.6772\) | |
466578.n2 | 466578n1 | \([1, -1, 0, -271476, -65983352]\) | \(-790993/216\) | \(-604226888328081816\) | \([]\) | \(7789824\) | \(2.1279\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466578.n have rank \(0\).
Complex multiplication
The elliptic curves in class 466578.n do not have complex multiplication.Modular form 466578.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.