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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 6006.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6006.j1 | 6006j2 | \([1, 0, 1, -12247, -468004]\) | \(203124303447538537/23341114298502\) | \(23341114298502\) | \([2]\) | \(21504\) | \(1.2972\) | |
6006.j2 | 6006j1 | \([1, 0, 1, 1063, -36760]\) | \(133018079080823/663548801916\) | \(-663548801916\) | \([2]\) | \(10752\) | \(0.95064\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6006.j have rank \(0\).
Complex multiplication
The elliptic curves in class 6006.j do not have complex multiplication.Modular form 6006.2.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.