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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 486720j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486720.j2 | 486720j1 | \([0, 0, 0, -184548, -23762752]\) | \(21952/5\) | \(158324327278940160\) | \([2]\) | \(6230016\) | \(2.0129\) | \(\Gamma_0(N)\)-optimal* |
486720.j1 | 486720j2 | \([0, 0, 0, -975468, 350500592]\) | \(405224/25\) | \(6332973091157606400\) | \([2]\) | \(12460032\) | \(2.3594\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 486720j have rank \(0\).
Complex multiplication
The elliptic curves in class 486720j do not have complex multiplication.Modular form 486720.2.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 Cremona 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 Cremona labels.