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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 6600.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6600.u1 | 6600ba1 | \([0, 1, 0, -283, -562]\) | \(10061824/5445\) | \(1361250000\) | \([2]\) | \(3072\) | \(0.44363\) | \(\Gamma_0(N)\)-optimal |
6600.u2 | 6600ba2 | \([0, 1, 0, 1092, -3312]\) | \(35969456/22275\) | \(-89100000000\) | \([2]\) | \(6144\) | \(0.79021\) |
Rank
sage: E.rank()
The elliptic curves in class 6600.u have rank \(1\).
Complex multiplication
The elliptic curves in class 6600.u do not have complex multiplication.Modular form 6600.2.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.