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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 422370u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422370.u2 | 422370u1 | \([1, -1, 0, 257145, -143042499]\) | \(1480374667773/7809152000\) | \(-9919487763978624000\) | \([2]\) | \(6912000\) | \(2.3272\) | \(\Gamma_0(N)\)-optimal* |
422370.u1 | 422370u2 | \([1, -1, 0, -3035175, -1828051875]\) | \(2434387065713667/271329500000\) | \(344653254957316500000\) | \([2]\) | \(13824000\) | \(2.6738\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 422370u have rank \(1\).
Complex multiplication
The elliptic curves in class 422370u do not have complex multiplication.Modular form 422370.2.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 Cremona 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 Cremona labels.