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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 481650.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
481650.g1 | 481650g4 | \([1, 1, 0, -4087775, -3182169375]\) | \(100162392144121/23457780\) | \(1769159744125312500\) | \([2]\) | \(23592960\) | \(2.4919\) | |
481650.g2 | 481650g3 | \([1, 1, 0, -1890775, 972357625]\) | \(9912050027641/311647500\) | \(23504108716054687500\) | \([2]\) | \(23592960\) | \(2.4919\) | \(\Gamma_0(N)\)-optimal* |
481650.g3 | 481650g2 | \([1, 1, 0, -285275, -37501875]\) | \(34043726521/11696400\) | \(882129512306250000\) | \([2, 2]\) | \(11796480\) | \(2.1453\) | \(\Gamma_0(N)\)-optimal* |
481650.g4 | 481650g1 | \([1, 1, 0, 52725, -4039875]\) | \(214921799/218880\) | \(-16507686780000000\) | \([2]\) | \(5898240\) | \(1.7987\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 481650.g have rank \(0\).
Complex multiplication
The elliptic curves in class 481650.g do not have complex multiplication.Modular form 481650.2.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.