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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 90480u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90480.d4 | 90480u1 | \([0, -1, 0, 11504, 525760]\) | \(41102915774831/53367275520\) | \(-218592360529920\) | \([2]\) | \(230400\) | \(1.4374\) | \(\Gamma_0(N)\)-optimal |
| 90480.d3 | 90480u2 | \([0, -1, 0, -70416, 5178816]\) | \(9427227449071249/2652468249600\) | \(10864509950361600\) | \([2, 2]\) | \(460800\) | \(1.7840\) | |
| 90480.d2 | 90480u3 | \([0, -1, 0, -416016, -99054144]\) | \(1943993954077461649/87266819409120\) | \(357444892299755520\) | \([2]\) | \(921600\) | \(2.1306\) | |
| 90480.d1 | 90480u4 | \([0, -1, 0, -1035536, 405896640]\) | \(29981943972267024529/4007065140000\) | \(16412938813440000\) | \([2]\) | \(921600\) | \(2.1306\) |
Rank
sage: E.rank()
The elliptic curves in class 90480u have rank \(2\).
Complex multiplication
The elliptic curves in class 90480u do not have complex multiplication.Modular form 90480.2.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 Cremona 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 Cremona labels.
