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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 440818.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
440818.u1 | 440818u2 | \([1, -1, 1, -326079, 71525993]\) | \(1494447319737/5411854\) | \(13885336729452286\) | \([2]\) | \(4644864\) | \(1.9585\) | \(\Gamma_0(N)\)-optimal* |
440818.u2 | 440818u1 | \([1, -1, 1, -11209, 2128645]\) | \(-60698457/725788\) | \(-1862173438935292\) | \([2]\) | \(2322432\) | \(1.6119\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 440818.u have rank \(1\).
Complex multiplication
The elliptic curves in class 440818.u do not have complex multiplication.Modular form 440818.2.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.