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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 41280.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41280.u1 | 41280g2 | \([0, -1, 0, -521, 1545]\) | \(3825694144/2015625\) | \(8256000000\) | \([2]\) | \(27648\) | \(0.59446\) | |
41280.u2 | 41280g1 | \([0, -1, 0, 124, 126]\) | \(3268147904/2080125\) | \(-133128000\) | \([2]\) | \(13824\) | \(0.24788\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41280.u have rank \(1\).
Complex multiplication
The elliptic curves in class 41280.u do not have complex multiplication.Modular form 41280.2.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.