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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 4730k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4730.d1 | 4730k1 | \([1, -1, 1, -5582262, 5077966149]\) | \(-19237750463016353596082481/360317791790000000\) | \(-360317791790000000\) | \([7]\) | \(219520\) | \(2.4932\) | \(\Gamma_0(N)\)-optimal |
4730.d2 | 4730k2 | \([1, -1, 1, 40144188, -96077802411]\) | \(7154705394529607961737582319/8127389307855235414199390\) | \(-8127389307855235414199390\) | \([]\) | \(1536640\) | \(3.4662\) |
Rank
sage: E.rank()
The elliptic curves in class 4730k have rank \(1\).
Complex multiplication
The elliptic curves in class 4730k do not have complex multiplication.Modular form 4730.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.