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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4730.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4730.a1 | 4730c2 | \([1, 0, 1, -117418, 15476508]\) | \(179028606517430416921/66598400\) | \(66598400\) | \([2]\) | \(13536\) | \(1.2902\) | |
4730.a2 | 4730c1 | \([1, 0, 1, -7338, 241436]\) | \(-43688964783576601/26658734080\) | \(-26658734080\) | \([2]\) | \(6768\) | \(0.94361\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4730.a have rank \(0\).
Complex multiplication
The elliptic curves in class 4730.a do not have complex multiplication.Modular form 4730.2.a.a
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.