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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 37479.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37479.g1 | 37479d4 | \([1, 0, 1, -66810, 6640963]\) | \(37159393753/1053\) | \(934541376093\) | \([2]\) | \(120960\) | \(1.3986\) | |
37479.g2 | 37479d3 | \([1, 0, 1, -18760, -897121]\) | \(822656953/85683\) | \(76043977899123\) | \([2]\) | \(120960\) | \(1.3986\) | |
37479.g3 | 37479d2 | \([1, 0, 1, -4345, 94631]\) | \(10218313/1521\) | \(1349893098801\) | \([2, 2]\) | \(60480\) | \(1.0521\) | |
37479.g4 | 37479d1 | \([1, 0, 1, 460, 8141]\) | \(12167/39\) | \(-34612643559\) | \([2]\) | \(30240\) | \(0.70548\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37479.g have rank \(1\).
Complex multiplication
The elliptic curves in class 37479.g do not have complex multiplication.Modular form 37479.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.