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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 38640c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38640.l2 | 38640c1 | \([0, -1, 0, -196936, -33572864]\) | \(824899990643380516/312440625\) | \(319939200000\) | \([2]\) | \(138240\) | \(1.5580\) | \(\Gamma_0(N)\)-optimal |
38640.l1 | 38640c2 | \([0, -1, 0, -197856, -33242400]\) | \(418257395996078018/8023271484375\) | \(16431660000000000\) | \([2]\) | \(276480\) | \(1.9046\) |
Rank
sage: E.rank()
The elliptic curves in class 38640c have rank \(0\).
Complex multiplication
The elliptic curves in class 38640c do not have complex multiplication.Modular form 38640.2.a.c
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.