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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 203280eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.x4 | 203280eh1 | \([0, -1, 0, 496544, 179136256]\) | \(1865864036231/2993760000\) | \(-21723662169538560000\) | \([2]\) | \(3686400\) | \(2.3956\) | \(\Gamma_0(N)\)-optimal |
| 203280.x3 | 203280eh2 | \([0, -1, 0, -3375456, 1830157056]\) | \(586145095611769/140040608400\) | \(1016178607135589990400\) | \([2, 2]\) | \(7372800\) | \(2.7421\) | |
| 203280.x1 | 203280eh3 | \([0, -1, 0, -50420256, 137808446976]\) | \(1953542217204454969/170843779260\) | \(1239696082655743426560\) | \([2]\) | \(14745600\) | \(3.0887\) | |
| 203280.x2 | 203280eh4 | \([0, -1, 0, -18282656, -28544753664]\) | \(93137706732176569/5369647977540\) | \(38963851021265878794240\) | \([2]\) | \(14745600\) | \(3.0887\) |
Rank
sage: E.rank()
The elliptic curves in class 203280eh have rank \(1\).
Complex multiplication
The elliptic curves in class 203280eh do not have complex multiplication.Modular form 203280.2.a.eh
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.
