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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2550.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2550.j1 | 2550n2 | \([1, 0, 1, -16576, -489202]\) | \(1289333385625/482967552\) | \(188659200000000\) | \([]\) | \(10800\) | \(1.4390\) | |
2550.j2 | 2550n1 | \([1, 0, 1, -7201, 234548]\) | \(105695235625/14688\) | \(5737500000\) | \([3]\) | \(3600\) | \(0.88968\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2550.j have rank \(1\).
Complex multiplication
The elliptic curves in class 2550.j do not have complex multiplication.Modular form 2550.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.