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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 8550.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8550.j1 | 8550q2 | \([1, -1, 0, -176742, -14750834]\) | \(428831641421/181752822\) | \(258784779761718750\) | \([2]\) | \(107520\) | \(2.0380\) | |
8550.j2 | 8550q1 | \([1, -1, 0, 37008, -1712084]\) | \(3936827539/3158028\) | \(-4496489085937500\) | \([2]\) | \(53760\) | \(1.6914\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.j have rank \(1\).
Complex multiplication
The elliptic curves in class 8550.j do not have complex multiplication.Modular form 8550.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.