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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 273600.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.u1 | 273600u3 | \([0, 0, 0, -29556300, 61847638000]\) | \(3825131988299044/961875\) | \(718035840000000000\) | \([2]\) | \(15728640\) | \(2.8014\) | |
273600.u2 | 273600u2 | \([0, 0, 0, -1854300, 958642000]\) | \(3778298043856/59213025\) | \(11050571577600000000\) | \([2, 2]\) | \(7864320\) | \(2.4549\) | |
273600.u3 | 273600u1 | \([0, 0, 0, -229800, -19307000]\) | \(115060504576/52780005\) | \(615625978320000000\) | \([2]\) | \(3932160\) | \(2.1083\) | \(\Gamma_0(N)\)-optimal |
273600.u4 | 273600u4 | \([0, 0, 0, -144300, 2658382000]\) | \(-445138564/4089438495\) | \(-3052749478763520000000\) | \([2]\) | \(15728640\) | \(2.8014\) |
Rank
sage: E.rank()
The elliptic curves in class 273600.u have rank \(0\).
Complex multiplication
The elliptic curves in class 273600.u do not have complex multiplication.Modular form 273600.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.