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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 55545.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55545.u1 | 55545l1 | \([1, 0, 1, -760449, 254433247]\) | \(328523283207001/1109390625\) | \(164229627420140625\) | \([2]\) | \(608256\) | \(2.1674\) | \(\Gamma_0(N)\)-optimal |
55545.u2 | 55545l2 | \([1, 0, 1, -429824, 477142247]\) | \(-59323563117001/630142750125\) | \(-93283742211659236125\) | \([2]\) | \(1216512\) | \(2.5140\) |
Rank
sage: E.rank()
The elliptic curves in class 55545.u have rank \(0\).
Complex multiplication
The elliptic curves in class 55545.u do not have complex multiplication.Modular form 55545.2.a.u
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.