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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 476850.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.j1 | 476850j2 | \([1, 1, 0, -11175325255, -454718704458635]\) | \(885060275427673959429985/12245029632\) | \(2135458914267237292800\) | \([]\) | \(380712960\) | \(4.1016\) | |
476850.j2 | 476850j1 | \([1, 1, 0, -138762055, -616255315595]\) | \(1694355380269778785/39957339045888\) | \(6968317629297826411315200\) | \([]\) | \(126904320\) | \(3.5523\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 476850.j have rank \(0\).
Complex multiplication
The elliptic curves in class 476850.j do not have complex multiplication.Modular form 476850.2.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.